Lines that have the same slope are said to be parallel, and if the slope of one line is equal to the negative reciprocal of the slope of the other, the two lines are said to be perpendicular; otherwise, they are merely intersecting lines.
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
m = Δy/Δx = dy/dx = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line may be shown as
tan θ = Δy/Δx
A line's slope often indicates the steepness and direction of the line.
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m = Δy/Δx = dy/dx = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line may be shown as
tan θ = Δy/Δx
What is the nature of roots of quadratic equation 4x2 5x 3 0?
The nature of the roots of the quadratic equation 4x² - 5x + 3 is complex.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
4x² - 5x + 3
This is in the form of ax² + bx + c
a = 4
b = -5
c = 3
Now,
D = b² - 4ac
If D < 0 there will be complex roots.
Now,
D = (-5)² - 4 x 4 x 3 = 25 - 48 = -23
D < 0
This means,
The roots are complex.
Thus,
The equation has complex roots.
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Guided practice (page 4)
Previous page
Distance from the ground in floors
11+
10+
of
8+
74
1
...
C
8 9 10
Which of the following statements are true about the elevator? Select all that apply.
Elapsed time in seconds
The elevator stayed 3 floors above the ground initially, then went to a lower floor.
The elevator stayed 3 floors above the ground initially, then went to a higher floor.
The elevator appeared to be moving faster when going up than when going down.
The elevator stayed 7 floors above the ground for 2 seconds.
Hint
Submit Answer
The correct statements of the given statements are -
The elevator stayed 3 floors above the ground initially, then went to a lower floor.The elevator appeared to be moving faster when going up than when going down.What is a mathematical function, equation and expression?Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function
Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators
Equation : A mathematical equation is used to equate two expressions.
Given is the distance of the elevator from the ground in floors.
The elevator stayed 3 floors above the ground initially, then went to a lower floor.The elevator appeared to be moving faster when going up than when going down.Therefore, the correct statements of the given statements are -
The elevator stayed 3 floors above the ground initially, then went to a lower floor.The elevator appeared to be moving faster when going up than when going down.To solve more questions on functions, expressions and polynomials, visit the link below -
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24 / 18/9 + 4
I don’t understand how to solve the problem at all.
Answer:4.1
Step-by-step explanation:
What is the mode of 12345?
If we answer yes, then 1, 2, 3, 4, and 5. No phrase is used more than once in this passage. Therefore, there is currently no most prevalent phrase. Thus, this data does not contain a mode.
How can I locate the mode?The mode calculation is a rather simple process. Organize the numbers in a set in whatever order—from lowest to highest as well as highest to lowest—and then tally the frequency with which each number appears in the group. The mode is the one that shows up most frequently.
The purpose of mode calculation?When the mean, as well as median, as well as median cannot be employed, the mode informs us of the most prevalent value in categorical data. The mode provides insight into the location of a dataset's "center".
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What is a multiplicity example?
A multiplicity example in mathematics is when a function has multiple solutions to a given equation.
For example, when solving the equation x2 + 4x + 3 = 0, there are two solutions, x = -3 and x = -1. This means that the equation has a multiplicity of two. This can be seen in the graph of the equation, which has two points of intersection on the x-axis.
The multiplicity is a measure of how many solutions a given equation has. It can be determined by using the discriminant, which is the difference between the square of the coefficient of the highest degree term, and four times the product of the coefficients of the lower degree terms, and the constant. In the example above, the discriminant is 16 - 12, which is 4. The multiplicity of the equation is determined by the sign of the discriminant: if it is positive, the equation has two solutions; if it is zero, the equation has one solution; and if it is negative, the equation has no solutions.
The multiplicity of an equation can also be used to determine the nature of the graph of the equation. If the equation has a multiplicity of two, the graph is a parabola, which is a curved line that has two points of intersection on the x-axis. If the equation has a multiplicity of one, the graph is a line, which has only one point of intersection on the x-axis. If the equation has a multiplicity of zero, the graph is a circle, which has no points of intersection on the x-axis.
The concept of multiplicity is important in mathematics, as it can be used to determine the number of solutions an equation may have, as well as the nature of the graph of the equation. Knowing the multiplicity of an equation can help to simplify the process of solving the equation.
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Estimate fx and fy at point B. 70 50 30 y 4 - -30 2 С 10 B -10- 0 - 00 30 50 10 -10 A -70 -2 -20 -4 (Use decimal notation. Give your answer to one decimal place.)
It is difficult to accurately estimate the values of fx and fy at point B without more information. In order to estimate the values of the partial derivatives at a point, you typically need to have a contour map or some other representation of the function in the neighborhood of that point.
A contour map is a graphical representation of a function that shows the values of the function at different points in the xy plane. The lines on the map, called contour lines, represent the values of the function, and the spacing between the lines indicates the rate of change of the function.
To estimate the values of the partial derivatives at a point using a contour map, you can:
Identify the contour line that passes through the point of interest.Look for nearby points on the map that have coordinates that differ only in the x or y direction from the point of interest.Calculate the difference in the function values at these points and divide by the difference in the x or y coordinate, depending on which partial derivative you are estimating.For example, to estimate fx at point B, you could:
Identify the contour line that passes through point B.Look for nearby points on the map that have y-coordinates that are the same as point B but x-coordinates that are different.Calculate the difference in the function values at these points and divide by the difference in the x-coordinates to estimate fx at point B.Without a contour map or other representation of the function in the neighborhood of point B, it is not possible to accurately estimate the values of fx and fy.
Since the question is incomplete and there is no similar one found, the answer is general.
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Question 5
Ethan put $1,250 into a savings account. The account pays 4.5% simple interest on an annual basis. If he does not add or withdraw money
from the account, how much interest will he earn after 2 years? Round to the nearest cent.
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Answer:
To calculate the interest earned on a savings account, you first need to determine the interest rate per year and the time the money is invested. In this case, the interest rate is 4.5% and the time is 2 years.
The formula for simple interest is I=Prt, where I is the interest earned, P is the principal (the initial amount invested), r is the interest rate, and t is the time. Plugging in the values from the problem, we get I = 1250 * 0.045 * 2 = $112.50.
Therefore, Ethan will earn $112.50 in interest after 2 years if he does not add or withdraw any money from the account. Rounded to the nearest cent, this is $112.00.
Step-by-step explanation:
How long will it take to fill the pool if two hoses are used, one that fills at a rate of 40 gallons per hour and one that fills at a rate of 60 gallons per hour? 100 hours 150 hours 180 hours 200 hours.
It will take 180 Hours to fill the pool if both hoses are used.
In our question, one data is missing. You require the pool's volume or some information that enables you to calculate it. The same statement given by you is part of a problem where you know a series of data that shows the time required to fill the pool at different flow rates:
flow rate time
60 gal/h 300 h => 60 gal/h * 300 h = 18,000 gal
45 gal/h 400 h => 45 gal/h * 400 h = 18,000 gal
36 gal/h 500 h => 36 gal/h * 500 h = 18,000 gal
30 gal/h 600 h => 30 gal/h * 600 h = 18,000 gal
So for this pool to calculate (several times) that the volume is 18,000 gal.
You now possess two hoses, one of which has a flow rate of 40 gals per hour and the other of which has a flow rate of 60 gals per hour.
The total flow rate is the sum of the two flow rates"
total flow rate = 40 gal/h + 60 gal/h = 100 gal/h
And you just must divide the volume of the pool (18,000 gals) by the total flow rate (100 gal/h) to get the time to fill the pool:
time = volume / flow rate = 18,000 gal / 100 gal/h = 180 hours.
So, finally, our answer to fill the pool will be about 180 hours.
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flow rate time
60 gal/h 300 h => 60 gal/h * 300 h = 18,000 gal
45 gal/h 400 h => 45 gal/h * 400 h = 18,000 gal
36 gal/h 500 h => 36 gal/h * 500 h = 18,000 gal
30 gal/h 600 h => 30 gal/h * 600 h = 18,000 gal
So for this pool to calculate (several times) that the volume is 18,000 gal.
You now possess two hoses, one of which has a flow rate of 40 gals per hour and the other of which has a flow rate of 60 gals per hour.
The total flow rate is the sum of the two flow rates"
total flow rate = 40 gal/h + 60 gal/h = 100 gal/h
And you just must divide the volume of the pool (18,000 gals) by the total flow rate (100 gal/h) to get the time to fill the pool:
time = volume / flow rate = 18,000 gal / 100 gal/h = 180 hours.
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answer: "approximately nine years
explanation : if an investment scheme promises an 8% annual compounded rate of return, it will take approximately nine years (72 / 8 = 9) to double the invested money.
hope this helps!!
What is the nature of roots of 2x² 6x 3 0?
The roots of the given equation are real and distinct because the value of b2-4ac is greater than 0
where a, b, and c are the coefficients in the standard form of the quadratic equation ax²+bx+c=0
Given quadratic equation is 2x²-6x+3=0 on comparing with the standard form of the quadratic equation ax²+bx+c=0
We have a=2, b=(-6) ,c=3
Hence b²-4ac,
Here b²-4ac is also known as discriminant.
=(-6)²-(4×2×3)
=36-24
=12≥0
12 (Twelve) is obviously greater than zero (0)
here value of b²-4ac>0
Hence the nature of the roots of the given equation is real and distinct.
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Question
What is the nature of roots of 2x²- 6x+ 3= 0?
PLEASE HELP ASAP! 40 POINTS!
The talent show committee is anticipating selling 300 tickets to the talent show. They expect 180 adults to attend, and 120 children to attend. They hope to raise $1,440 from ticket sales to purchase classroom supplies. Adult tickets will be twice as expensive as child tickets. For what prices should the committee sell adult tickets and child tickets to the show?
Step-by-step explanation:
The committee should sell adult tickets for $10 and child tickets for $5 to raise $1,440 from ticket sales.
Let x be the price of adult tickets in dollars and y be the price of child tickets in dollars. We can set up the following system of equations to represent the given information:
x + y = 300 (the total number of tickets sold)
180x + 120y = 1440 (the total amount of money raised)
x = 2y (the price of adult tickets is twice the price of child tickets)
Substituting the third equation into the first equation, we get:
2y + y = 300
3y = 300
y = 100
Substituting this value for y into the third equation, we get:
x = 2*100
x = 200
Substituting these values for x and y into the second equation, we get:
180200 + 120100 = 1440
This equation is true, so the solution x = $200 and y = $100 is valid. Therefore, the committee should sell adult tickets for $10 and child tickets for $5 to raise $1,440 from ticket sales.
What is the inverse function calculator?
The inverse of the function that is provided is calculated using the inverse function calculator. When a function, f(x), is given, its inverse, x=f(y), is calculated by switching the variables ( y ).
Given,
Inverse function;
An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f1.
Inverse function calculator;
The calculator for inverse functions determines the inverse of the supplied function. If a function, f(x), is supplied, then the inverse of the function, x=f(y), is determined by exchanging the variables ( y ).
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A car travels 62 miles per hour. At this rate, how far will the car travel in 7 hours?
Answer:
372 miles
Step-by-step explanation:
You need to multiply 62 and 6
Answer:
The car will travel 434 miles in 7 hours.
Step-by-step explanation:
To get the answer you simply need to multiply 62, which is the speed of the car, by 7 hours, how long it will travel.
Therefore, the answer is 434 miles.
Determine the domain of the following graph
Answer:
-1
Step-by-step explanation:
I got -1 by getting two points from the graph where the line touches. The two points I got were (0,-3) and (1, -4). When it asks you to find the domain it's asking you to find for the slope. The domain and the slope are the same thing. To find slope you use the slope formula which is y2-y1 over x2-x1. Once you set up your equation you should get -4-(-3) over 1-0. When you solve it you should get -1/1 and -1 divided by 1 is -1. So then the slope is -1....
(hope you were able to understand it... I might've not chosen the right points but hopefully I did...I'm sorry if you get it wrong)
What is the range () function give example?
Here we can say that - A series of integers can be generated over time using the range() method.
What is Range?Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the variable and deduct the least observed value the minimum. The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.
given,
20, 25, 30, 45, 55, 90, 110,115,120
so range will be 120 - 20 = 100
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What is the maximum value of this function f x )= − 16x2 32x 20?
On solving the provided question, we can say that - the maximum value or maxima of the given function is 36.
What is maxima?Maximum describes a high point (plural maxima). The term "minimum" refers to a low point (plural minima). Extremum is the Latin term used to describe the greatest or minimum (plural extrema). When greater points are possible elsewhere but not close by, we say local maximum (or minimum). The greatest and smallest values of a function in either a specified range or throughout the whole domain are referred to as a function's maxima and minima, generally known as extrema, in mathematical analysis.
The vertex is used to determine that the function's maximum value is 36.
Function is provided by:
f(x) = [tex]16x^2 + 32x + 20[/tex]
coefficients -
[tex]a = -16, b = 32 , c =20[/tex]
[tex]f_{max} = \frac{32^2 - 4(-16)(20)}{4(-16)}[/tex] = 36
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Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 12 feet and a height of 19 feet. Container B has a diameter of 14 feet and a height of 13 feet. Container A is full of water and the water is pumped into Container B until Conainter B is completely full.
After the pumping is complete, what is the volume of the empty space inside Container A, to the nearest tenth of a cubic foot?
After the pumping is complete, the volume of the empty space inside container [A] will be 1147.72 ft³.
What is volume of a cylinder? What is equation modelling? What is a mathematical equation and expression?The volume of the cylinder is equivalent to -v{c} = πr²h = π(d/2)²h
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Given are two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 12 feet and a height of 19 feet. Container B has a diameter of 14 feet and a height of 13 feet. Container A is full of water and the water is pumped into Container B until Container B is completely full.
Volume of container [A] -
V{A} = (22/7) x (12/2)² x 19
V{A} = (22/7) x 6 x 6 x 19
V{A} = 3149.72 ft³
Volume of container [B] -
V{A} = (22/7) x (14/2)² x 13
V{A} = (22/7) x 7 x 7 x 13
V{B} = 2002 ft³
V{A} - V{B} → Empty space = 3149.72 ft³ - 2002 ft³ = 1147.72 ft³
Therefore, the free space inside the container A will be 1147.72 ft³.
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3. Mary is a real estate agent. One month she sold 7 houses at these prices: $171 000, $165 000, $178 000, $161 000, $174 000, $168 000, $240 000
3.a) What is the median price of the houses she sold?
3.b) Do you think the mean price is greater than or less than the median price of the houses sold that month? Why?
3.c) Which average do you think better represents a typical price of houses she sold that month? Why?
The median price of the houses sold will be equal to $171000 and yes, the mean price is greater than the median price of the houses.
What is Mean?Mean in mathematics is a quantity that falls somewhere between the extremes of a set. There are different types of meanings, and how they are calculated relies on the connection that is known about or is believed to control the other members.
a.
The median of given prices will be,
Let's arrange the given prices in ascending order,
161000, $165000, $168000, $171000, $174000, $178000, $240000
Then, the middle term is the median,
So, median = $171000
b.
Number of terms = 7
The mean of the given prices will be,
(171000 + 165000 + 178000 + 161000 + 174000 + 168000 +240000)/7
= 1257000/7
Mean = 179571.4286
Comparing mean and median, the mean price is greater than the median.
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How many of these numbers are divisible by 3?
The numbers which are divisible by 3 are countless. We determine it by the divisibility rules.
What is divisible in mathematics?
A number is called divisible by others whenever it is divided properly and obtain a whole number as an outcome. As example 125 can be divided by 5 and we get the whole number 25 so 125 is said divisible by 5.
On the other hand, 225 cannot be divided by 10 and we get a decimal number. So, 225 is not divisible by 10.
How many numbers are divisible by 3?A number is said to be divisible by 3 if the sum of the digits is divided by 3. Suppose we are given two number 308 and 492.
At first, we will sum the digit of each number, 3+0+8 = 11
the sum of the digit of 492 = 4+9+2 = 15
we cannot divide 11 by 3 but 15 is divided by 3. Hence, 492 is divisible by 3.
So, there are countless number which are divisible by 3.
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Can you do formulas in prism?
The formula for a prism is as follow,
The surface area of a prism = (2×Base Area) +Lateral Surface Area
The volume of a prism =Base Area× Height
A prism is a solid whose perimeter is defined by a number of congruent parallel plane polygons, two of which are known as the ends, and two of which are known as the side faces.
The polyhedron known as a prism has two parallel polygonal bases. A prism is a transparent optical device with flat, polished surfaces that refract light. The two polygonal bases are connected by their lateral faces. Longitudinally, the faces are primarily rectangular. It could even be a parallelogram occasionally.
The surface area of a prism is made up of the combined areas of the lateral faces and the two polygonal bases.
The total area that a prism takes up in three dimensions is known as its volume.
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How do you find the mean and standard deviation of a random variable?
Random variable contains the random outcome of an event in probability, The mean and standard deviation are calculated in terms of expected values E(x) in case of random variable.
What do you mean by random variable?The mathematical formalization of a number or object that is subject to chance events is known as a random variable. It is a function or mapping between a space of potential outcomes, commonly real numbers, to a space of measurement.
What is mean and standard deviation?The arithmetic mean, also known as the arithmetic average or simply the mean or average, is the sum of a set of numbers divided by the total number of numbers in the set. The collection frequently consists of a series of findings from a survey, experiment, or observational study.
The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
for a random variable, we use expected value for mean and standard deviation.
mean = E(X)
Standard deviation = [tex]\sqrt {variance} =\sqrt {E(X^{2})-(E(X)^{2})}[/tex]
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Three people build a rectangular shed 6 m wide, 4 m long, and 5 m high. How many cubic meters is the shed?.
120 m³ is cubic meters is the shed.
Given :
What in math is a cube?
The term "cube" refers to a solid three-dimensional shape in mathematics or geometry that has six square faces, eight vertices, and twelve edges. Also said to be a conventional hexahedron. Due to the fact that a cube is three dimensional, the space it occupies will also be three dimensional.
Six square faces surround a cube, hence combining the areas of all six square faces will yield the surface area. The cube formula's surface area is as a result. Cube surface area equals 6 (sides).
w = 6 m
l = 4 m
h = 5 m
a rectangular shed = 6 * 4 * 5
= 120 m³
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f(x) = 10 –
f(134) :
X
134
Answer: -1/34
Step-by-step explanation:
Answer:
f(134) = 9
Step-by-step explanation:
substitute x = 134 into f(x) and evaluate
f(x) = 10 - [tex]\frac{x}{134}[/tex] , then
f(134) = 10 - [tex]\frac{134}{134}[/tex] = 10 - 1 = 9
What is the mean of the given set of data 12 20 8 15 16 14 7 5 11 8 14?
11.81 is the required mean of the given data set.
What is mean?The mean (also known as the arithmetic mean, which varies from the geometric mean) of a dataset is calculated as the sum of all values divided by the total number of values.
This measure of central tendency is usually referred to as the "average".
Thus, the data set is as follows:
12, 20, 8, 15, 16, 14, 7, 5, 11, 8, 14
Mean formula: Sum of terms / Number of terms
The mean will now be determined as follows:
Mean: Sum of terms / Number of terms
Mean: 130/11
Mean: 11.81
Therefore, 11.81 is the required mean of the given data set.
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In which triangle all the sides are equal and all the angles are also equal *?
brine flows into a conical tank at a constant rate of 3 cubic feet per minute. the radius of the cone is 5 feet and its height is 12 feet. how fast is the radius increasing when the radius is 2 feet?
Applying derivative on the formula of volume of cone and using the provided values, The answer is 0.059 feet per minute.
What do you mean by derivative?The rate at which a function changes in relation to a variable in mathematics.
What is a cone and it's formula for volume?A cone is a three-dimensional geometric structure with a smooth transition from a flat base often but not always circular to the point at the top, also known as the apex or vertex.
Formula for volume of cone is:
[tex]V= \pi r^{2}\frac{h}{3}[/tex]
derivate the formula for volume of cone , we get,
[tex]\frac{dV}{dt} = 2\pi r * \frac h3 * \frac {dr}{dt}[/tex]
dV / dt = 3
r=2
h=12
dr/dt = 0.059 feet per minute.
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Do the one you would like please show work
Step-by-step explanation:
I am not what the answer My teacher
What is set and example?
Set is the collection of objects with defined property and represented in curly brackets {} . Example: A = { 2, 4, 6 }.
Set is defined as:
The collection of objects in an organized manner with some defined property.It is represented by curly brackets {}.Two ways to represents the given set is set builder form and the roaster form.If we defined collection of books it is not considered as set as here no well defined property is mentioned.If it is collection of books written by any particular writer than it is a set.Example of set is defined as collection of even numbers less than 8 is written as A = { 2. 4, 6 }Learn more about set here
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How do you find the maximum value of a parabola using calculus?
You can use calculus to find the maximum value of a parabola by these steps which are given in the solution part.
What is Parabola?A parabola is a U-shaped curve this is drawn for a quadratic function,
To find the maximum value of a parabola using calculus, you can follow these steps:
1. Identify the equation of the parabola in the form "y = ax² + bx + c," where "a," "b," and "c" are constants.
2. Take the derivative of the equation with respect to x.
3. Set the derivative equal to 0 and solve for x. This will give you the value of x at the vertex of the parabola.
Substitute the value of x that you found in step 3 back into the original equation to find the corresponding y-value. This y-value is the maximum or minimum value of the parabola, depending on the value of a. If a is positive, the parabola opens upwards and the y-value is the maximum. If a is negative, the parabola opens downwards and the y-value is the minimum.
For example, suppose you want to find the maximum value of the parabola y = 2x² - 4x + 3. First, take the derivative of the equation: y' = 4x - 4. Set this equal to 0 and solve for x: 0 = 4x - 4, x = 1.
Substituting this value back into the original equation gives us y = 2(1)² - 4(1) + 3 = 2 - 4 + 3 = 1.
Therefore, the maximum value of the parabola is 1.
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