Create a hand drawn sketch of the quadratic function: h(x)= -2x^2 +5x-8To earn full credit be sure to identify the vertex, the axis of symmetry and all intercepts. Include all work, calculations and steps needed (as described in this lesson) to create the graph.Let your teacher know if you have any questions on how to upload or share your written work.
Answers
Hello!
We have the function below:
[tex]h\mleft(x\mright)=-2x^2+5x-8[/tex]The first step is to identify the coefficients a, b and c:
• a = -2
,• b = 5
,• c = -8
Just by analyzing these coefficients, we can say that the concavity of the parabola will be facing downwards because the coefficient a is negative
1st step: using the quadratic formula, we will find the interceptions in the x-axis. Look:[tex]x=\frac{-b\pm\sqrt[]{b^2-4\cdot a\cdot c}}{2\cdot a}[/tex]As we know the coefficients, let's replace them in the formula:
[tex]\begin{gathered} x=\frac{-5\pm\sqrt[]{5^2-4\cdot(-2)\cdot(-8)}}{2\cdot(-2)} \\ \\ x=\frac{-5\pm\sqrt[]{25^{}-64}}{-4}=\frac{-5\pm\sqrt[]{-39}}{-4}= \end{gathered}[/tex]Obs: as we obtained a negative square root, we can stop this step here. It means that
2nd step: let's identify the maximum point of it:[tex]\begin{gathered} x_V=\frac{-b}{2\cdot a}=\frac{-5}{2\cdot(-2)}=\frac{-5}{-4}=1.25 \\ \\ y_V=-\frac{b^2-4\cdot a\cdot c}{4\cdot a}=-\frac{5^2-4\cdot(-2)\cdot(-8)}{4\cdot(-2)}=-\frac{-39}{-8}=-4.875 \end{gathered}[/tex]So, the vertex is at the point (x, y) = (1.25, -4.875).
The axis of symmetry is x = 5/4 or also x = 1.25.
Look at the graph below:
Note: if you solve this function when x = 0, you will obtain one interception in the y-axis, look:
[tex]\begin{gathered} h\mleft(x\mright)=-2x^2+5x-8 \\ h\mleft(0\mright)=-2\cdot0^2+5\cdot0-8 \\ h(0)=0+0-8 \\ h(0)=-8 \end{gathered}[/tex]So, the y-intercept is at (x, y) = (0, -8) as you can see at the graph.
Related Questions
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
600
Step-by-step explanation:
[tex]R(1)=400 \\ \\ R(2)=1000 \\ \\ R(2)-R(1)=600[/tex]
PLEASE HELP GEOMETRY 50 POINTS
Answers
Answer:
See below
Step-by-step explanation:
Alternate exterior angles are equal if the lines crossed by the transversal are parallel
15x + 9 = 21x - 27
9 + 27 = 21x - 15 x
x = 6 °
Thousandths Chart The students in Ms. Lowell's class wrote a thousandths decimal chart on the board. 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01 0.011 0.012 0.013 0.014 0.015 0.016 0.017 0.018 0.019 0.02 Describe the pattern in the table above for moving across a row from left to right.
Answers
Answer:
the pattern is that the next number in the row is obtained by adding 0.001 to the previous number
Step-by-step explanation:
Difference between consecutive numbers as you go from left to right is an increase of 0.001
So the pattern is that the next number in the row is obtained by adding 0.001 to the previous number
Three-fourths of a box of chocolate is left over. Benjamin eats 2/3 of the leftover chocolate. What fraction of a box does Benjamin eat?
Answers
We will have that he ate the following amount:
So, he ate the following:
[tex]x=(\frac{3}{4})(\frac{3}{4})\Rightarrow x=\frac{1}{2}[/tex]He ate a total of 1/2 of the chocolate.
Carter budgets
18
% of his salary for food. His salary is $
3
,
900
. How much money does he need to budget for his food?
Answers
Answer:
3900*18%=702
Step-by-step explanation:
Explain why the value of the sine ratio for an acute angle
of a right triangle must always be a positive value less
than 1.
Answers
The sine is defined as the length of the opposite side divided by the length of the hypotenuse, both of which are positive. Since dividing a positive number by a positive number results in a positive number, the sine must be positive.
Also, since the hypotenuse is the longest side of the triangle, the sine is equal to some positive number less than the length of the hypotenuse being divided by the length of the hypotenuse, resulting in a number less than 1.
If A(2, 2), B(6, 4), C(4, 4) and D(8, 6) are four points then prove that: AB= CD
Answers
THE ONLY WAY WE CAN PROVE THAT AB IS EQUAL CD IS BY CALCULATING THE DISTANCES AND THEN COMPARING THEM.
FOR AB
[tex] = \sqrt{( {x2 - x1})^{2} + ( {y2 - y1})^{2} } \\ = \sqrt{(( {6- 2})^{2} + ( ({4 - 2})^{2} } \\ = \sqrt{( {4})^{2} +( {2})^{2} } \\ = \sqrt{16 + 4} \\ = \sqrt{20} [/tex]
THE DISTANCEAB IS GIVEN ABOVE.
NOW LET US CALCULATE DISTANCE CD
[tex] = \sqrt{ ({8 - 4)}^{2} + ({6 - 4})^{2} } \\ = \sqrt{ {(4})^{2} + ({2})^{2} } \\ = \sqrt{16 + 4} \\ = \sqrt{20} [/tex]
WE CAN SEE THAT DISTANCE AB AND DISTAMCE CD ARE EQUAL THERE SE CAN NOW SAY
AB=CD
What is the compound interest earned on a $10,000 investment that earns 6% compounded monthly for 5 years?
Answers
Use the DistributiveProperty to express40 + 56
Answers
Answer:We want to use distributive property to express:
Using distributive property,
[tex]40+56=8\times5+8\times7[/tex]Explanation:
[tex]40+56[/tex]8 is a common factor of 40 and 56, so we can write:
as
[tex]\begin{gathered} 8\times5=40 \\ \text{and} \\ 8\times7=56 \end{gathered}[/tex]S
[tex]40+56=8\times5+8\times7[/tex]a class has 30 cups of popcorn. they are filling individual bags with three-fourths cups of popcorn. write a number sentence to show how many bags they can fill with popcorn
Answers
If the clas has 30 cups and fills individual bags with three-fourths cups then the number of bags that can be filled
= 30 / (3/4)
= 30 * 4/3
= 40
Hence 40 bags can be filled with popcorn
(a) It takes 36 pounds of seed to completely plant a 6-acre field. How many pounds of seed are needed per acre?
Answers
Answer:
6
Step-by-step explanation:
The answer would be 6 since it would take 36 pounds of seed to plant a 6 acre field. That means you would need 6 pounds of seed for each acre since 36 ÷ 6 = 6
Need help with this question! Need help with showing work.
Answers
From the 2014-2015 to 2024-2025, the number of student enrolled in an associate degree program is projected to increase by 23.5%. If the enrollment in associate degree in 2014-2014 is 6,600,000, find the increase and the projected number of students in an associate degree program in 2024-2025
Answers
Given,
From the 2014-2015 to 2024-2025, the number of student enrolled in an associate degree program is projected to increase by 23.5%.
The enrollment in associate degree in 2014 is 6,600,000.
The increase and the projected number of students in an associate degree program in 2024-2025 is,
[tex]\begin{gathered} \text{Increase in number of students= total students in 2014}\times\frac{percentage}{100} \\ =6600000\times\frac{23.5}{100} \\ =66000\times23.5 \\ =1551000 \end{gathered}[/tex]Hence, the increase and the projected number of students in an associate degree program in 2024-2025 is 1551000.
In a survey of 100 patients who reported at the hospital one day, it was found out that 70 of them complained fever, 50 complained stomach pains and 30 were injured. All 100 patients had at least all the complaints and 44 had exactly two of the complaints. How many patients had all the complaints?
Answers
Three patients had all the complaints.
What is a Set's Cardinal Number?In a finite set, the number of distinct elements is known as the cardinal number. It is written as n(A) and can be read as "the number of set elements."
Let's assume,
U is the set of patients who reported at the hospital on that day.
F is the set of patients who complained of fever.
S is the set of patients who had stomach troubles.
I is the set of injured patients.
The given data can be written as follows:
n(U) = n(F∪S∪I) = 100
n(F) = 70
n(S) = 50
n(I) = 30
n(F∩S) + n(S∩I) + n(I∩F) - 3×n(F∩S∩I) = 44
Using the cardinal number of the union of three sets formula, we get
n(F∪S∪I) = n(F) + n(S) + n(I) - n(F∩S) - n(S∩I) - n(I∩F) + n(F∩S∩I)
100 = 70 + 50 + 30 - (44 + 3×n(F∩S∩I)) + n(F∩S∩I)
100 = 150 - 44 - 2×n(F∩S∩I)
2×n(F∩S∩I) = 106 - 100 = 6
n(F∩S∩I) = 3
Therefore, 3 patients had all the complaints.
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Solve each of the following equations using the Extended Square Root Property.
1. 8√x+7=16
x= _____________
2. √7x+4−3=0
x= _____________
3. 8√5x−7=16
x= _____________
Answers
Answer:
1. 81/16, 2. DNE(undefined), 3. 529/64
Step-by-step explanation:
[tex]1. \\8\sqrt{x} +7=16\\\\8\sqrt{x} =16-7-9\\\sqrt{x}=9/8\\x=(9/8)^2=81/64\\\\2.\\1. \\\sqrt{7x} +4-3=0\\\\\sqrt{7x} +1=0\\\sqrt{7x}=-1\\[/tex]
impossible because square root is always positive
[tex]3. \\8\sqrt{5x} -7=16\\8\sqrt{5x} =16+7=23\\\\\sqrt{5x} =23/8\\\\5x=(23/8)^2=529/64[/tex]
What is the square root of the product of m and n
Answers
The square root of the product of m and n is √mn.
What are square roots?The value that, when multiplied by itself, returns the original number is called the square root of any number. The sign "√" is used to denote it. There are two square roots for every number, one of which has a positive value and the other a negative value. For instance, the number 4 has 2 and -2 as its two square roots.Any number's square root is represented as the number raised to the power 1/2. The following is the square root formula for the number x.[tex]\sqrt{x} = x^{1/2}[/tex]
To determine the square root of the product of m and n, find the product of m and n and raise the product to the power 1/2.
Product of m and n = mn
The square root of the product is = [tex](mn)^{1/2} = \sqrt{mn}[/tex]
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Two students attempted to solve the literal equation[tex]a=1\fra/2(b+c)[/tex]
for c. Who solves it correctly? How do you know?
Answers
. Length of the rectangular prism is 4 ft. The height and width are both 3 feet. Find the surface area of the prism.
Answers
Ok, so
Here we have a rectangular prism with the following measures:
-Length = 4ft
-Height = 3ft
-Width = 3ft.
Remember that the surface area of a rectangular prism can be found using:
[tex]SA=2lw+2wh+2lh[/tex]Where "l" is the length, "w" is the width, and "h" is the height.
If we replace our values in the equation given, we got that:
[tex]\begin{gathered} SA=2(4)(3)+2(3)(3)+2(4)(3) \\ SA=24+18+24 \\ SA=66 \end{gathered}[/tex]Therefore, the surface area of the prism is 66 ft2.
If rocks along the furnace creek fault have been offset 30 miles over 10 million years, what is the rate of plate motion in cm/year. (Hint: Rate x Time = Distance, and there are 5280 feet in one mile, and 2.54 cm. in one inch.)
Answers
The rate of plate motion in cm/year is equal to 3.3528 × 10⁻³ cm/year.
What is a conversion factor?A conversion factor can be defined as a number that is typically used to convert (change) a number in one (1) set of units to another, either by dividing or multiplying.
Generally speaking, an appropriate conversion factor to an equal value must be used when it is necessary to perform any mathematical conversion.
Conversion:
1 mile = 5280 feet
30 miles = X feet
Cross-multiplying, we have:
X = 30 × 5280
X = 158,400 feet.
Next, we would convert the value in feet to inch and then to cm as follows:
Distance = 158,400/12 = 13,200 inches.
In centimeters (cm), we have:
1 inch = 2.54 cm
13,200 inches = Y cm
Cross-multiplying, we have:
Distance, Y = 13,200 × 2.54
Distance, Y = 33,528 cm.
Now, we can determine the rate of plate motion in cm/year:
Rate = Distance/Time
Rate = 33,528/10,000,000
Rate = 3.3528 × 10⁻³ cm/year.
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5x 4091+921
What will it be be
Cause hard
Answers
An easy way to find it is by multiply each number by 5 or by using a calculator.
4091
X. 5
20455
2) Next add the 921
20455 + 921 = 21376
3) Answer is 21376
One leg of a right triangle is 8 inches less than the hypotenuse. The other leg is 12 inches. Find the length of hypotenuse.
Answers
Answer:
13 in
Step-by-step explanation:
Let the hypotenuse be x. Then, by the Pythagorean theorem,
[tex](x-8)^2 + 12^2=x^2 \\ \\ x^2-16x+64+144=x^2 \\ \\ 16x=64+144 \\ \\ x=4+9 \\ \\ x=13[/tex]
Solve each system of equations algebraically.
x + y = 3
- 2x + y = -6
How do you solve this, I can't seem to comprehend this, its hard for me. ;
Answers
The solution to the system of equation is the point where both lines intersect and it is at (3, 0)
System of equations
Given the following system of equations
x + y = 3
- 2x + y = -6
Graphically, the point where both lines intersect on the place is the solution to the given system of equation.
From equation 1, x = 3 - y
Substitute into equation 2:
- 2(3-y) + y = -6
-6 + 2y + y = -6
3y = -6 + 6
y = 0
Substitute y = 0 into any of the equation
x + y = 3
x + 0 = 3
x = 3
Hence the solution to the given system of equation is (3, 0)
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Write a quadratic function for the following characteristics
Answers
Answer:
[tex]y=x^2+6x-16[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a quadratic equation}\\\\$y=a(x-p)(x-q)$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the $x$-intercepts. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
Given points on the curve:
(-8, 0)(-6, -16)(2, 0)The x-intercepts of a quadratic function are the points at which the line crosses the x-axis, so when y = 0.
Therefore, the x-intercepts of the given function are -8 and 2.
Substitute these into the intercept formula:
[tex]\implies y=a(x-(-8))(x-2)[/tex]
[tex]\implies y=a(x+8)(x-2)[/tex]
Substitute the other given point (-6, -16) into the equation and solve for a:
[tex]\begin{aligned} y&=a(x+8)(x-2)\\\textsf{When }(-6,-16)\implies -16&=a(-6+8)(-6-2)\\-16&=a(2)(-8)\\-16&=-16a\\\implies a&=1\end{aligned}[/tex]
Therefore, the equation of the function in intercept form is:
[tex]y=(x+8)(x-2)[/tex]
Expand to standard form:
[tex]\implies y=x(x-2)+8(x-2)[/tex]
[tex]\implies y=x^2-2x+8x-16[/tex]
[tex]\implies y=x^2+6x-16[/tex]
Therefore, the quadratic function in standard form is:
[tex]\boxed{ y=x^2+6x-16}[/tex]
Are the ratios 5:4 and 18:16 equivalent
Answers
Consider them in the form of fractions: 5/4 is in simplest form, and 18/16 cannot simplify to 5/4. Therefore, the two ratios are not equivalent.
Trisha is making flags with 40 5/16 yards of fabric. If each flag requires 3 1/8 yards, how many flags can she make?
Answers
Answer:
I just wanted points please forgive me
Step-by-step explanation:
hvxjdfcdhd
I'm safe 35% of 400 he needs to save to buy a bike how much money has Adam saved so far
Answers
∵ The percentage of the saving is 35%
∵ The total money is 400
→ Multiply 35% by 400 to fin
Simplify the fraction
18
60
as much as possible.
3
10
18
60
12
54
Answers
Answer:
3/10
Hope this helps!
Have a good day :)
Graph the following Absolute Value Functions.
Analyze when the function is positive, negative,
increasing, or decreasing. Then describe the end
behavior of the function.
▶1. f(x) = x+3/+2
2. f(x)=x-7/+2
3. f(x) = -x-4-9
4. f(x) = x+8 -1
5. f(x) = 3|x-1| +5
6. f(x) = -x +4+3
7. f(x) = -x-6-10
8. f(x) = -2/x+2-8
Help please
Answers
The absolute value of the given functions are ;
1. increasing
2. increasing
3. decreasing
4. increasing
5. increasing
6. decreasing
7. decreasing
8. decreasing
What are increasing and decreasing functions?Calculus functions called increasing and decreasing functions have f(x) values that change according to how much x rises or decreases. The behavior of growing and decreasing functions is examined using the derivative of the function f(x). If the value of f(x) grows as the value of x increases, the function is said to be increasing; conversely, if the value of f(x) decreases as the value of x increases, the function is said to be declining.
Like wise in this question we just have to find the d/dx and if it comes out positive then the function is increasing and if it is negative then it is decreasing.
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Calculate both outliers
Answers
The outlier for Hits in league A is 40
The outlier for Hits in league B is 260
What is an outlier?An outlier can simply be defined as a data point that varies enormously or significantly from other recorded observations in a data set.
It occurs due to certain variability in the measurement of a data set or research.
It is known as an indicator of experimental errors.
It is also known to be the cause serious of errors in statistical analyses.
From the images shown, we have;
For Hits in league A;
The data set is; 20 - 40, 100 - 120, 120 - 140, 140 - 160, 160 - 180, 180 - 200, 200 - 220
We can see that the outlier is 40
For Hits in league B;
The data set is; 120 - 140, 140 - 160, 160 - 180, 180 - 200, 200 - 220, 240 - 260
The outlier is 260
Hence, the outliers are 40 and 260
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susan says that (-3)(-3)(-3) will be a positive answer. ryan says that the product will be a negative answer. who is correct use words and numbers in your response
Answers
Answer: Ryan is correct
Step-by-step explanation:
-3 multiplied by -3 makes a positive 9. Then you need to multiply that 9 by the other -3 which makes it a negative 27.
(-3) x (-3) x (-3)
9 x -3
-27