Steps for graphing a quadratic equation from vortex form
Answers
Graphing a Quadratic Equation
Let's take as an example the function:
[tex]y=-2\mleft(x-3\mright)^2+5[/tex]The vertex form of a quadratic function is:
[tex]y=a\mleft(x-h\mright)^2+k[/tex]Where a is the leading coefficient and (h,k) is the vertex.
If a is positive, the function is concave up, if negative the function is concave down.
The first step is to obtain the parameters by comparing the given equation with the general equation.
Thus, we have: a = -2. Vertex = (3,5)
Now we locate the vertex in the coordinate plane and draw the parabola opening down.
For more precision, we can substitute some points around the vertex, like for example:
x={1,2,4,5}
We get the y-coordinates:
y={-3,3,3,-3}
Then we plot the graph as follows:
Related Questions
the three sided lengths are 7,8,9 classify the triangle as an acute obtuse or right triangle
Answers
Using the law of cosines to find m∠B:
[tex]\begin{gathered} b^2=a^2+c^2-2ac\cdot\cos (B) \\ 2ac\cdot\cos (B)=a^2+c^2-b^2 \\ \cos (B)=\frac{a^2+c^2-b^2}{2ac} \\ \cos (B)=\frac{8^2+7^2-9^2}{2\cdot8\cdot7} \\ \cos (B)=\frac{32}{112} \\ B=\arccos (\frac{32}{112}) \\ B=73.4\text{ \degree} \end{gathered}[/tex]Since B is the largest angle (because it's opposite to the longer side), then angles A and C are smaller. In consequence, the three angles are smaller than 90°, which means that the triangle is acute
Write an equation that represents the line.
Use exact numbers.
Answers
Answer:
y=0.75x+2
Step-by-step explanation: Slope as k and constant as b two points that showed by the graph: (0,2) (4,5)
so we can get 2=0*k+b b=2
5=4k+b
4k=5-2
4k=3
k=3/4
k=.75
P = 1,000 m
X =
x m
150 m width
Answers
Answer:tiny bit confused what the question is asking
length=350
Step-by-step explanation:
perimeter =(length+width )x2
perimeter/2
1000/2=(length+width )
500=(length+width)
500-150=350length
17. MTR Model Problems Place points on the number line to show 4 equal lengths from 0 to 1.8. How long is each length?
Answers
Answer:
4.5
Step-by-step explanation:
4.5 + 4.5 + 4.5 + 4.5 = 18
You write it like this in the number line:
4.5, 9, 13.5, 18
Ann and Tom want to establish a fund for their grandson's education. what lump sum must they deposit at a 7% annual interest rate compounded monthly in order to have $60,000 in the fund at the end of 10 years?
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Formula to calculate Principal with clompound interest:
[tex]\begin{gathered} P=\frac{A}{(1+\frac{r}{n})^{n\cdot t}} \\ \\ A=\text{Amount} \\ r=\text{Interest rate (decimals)} \\ n=\text{ number of times per unit t} \\ t=time \end{gathered}[/tex]For the given situation:
A= 60,000
r= 7% =7/100= 0.07
n= 12 (as it is compounded monthly and a year has 12 months)
t= 10 years
[tex]\begin{gathered} P=\frac{60,000}{(1+\frac{0.07}{12})^{12\cdot10}} \\ \\ =\frac{60,000}{(1+\frac{0.07}{12})^{120}} \\ \\ \approx29,855.78 \end{gathered}[/tex]Then, they must deposit approximately $29,855.75
A backpack weighs 10 N. What is the mass of the backpack?
Answers
The mass of the backpack is 1.02 kilograms.
What is the mass of the backpack?On earth, the weight of an object of mass M is given by:
W = M*g
Where g is the gravitational acceleration:
g = 9.8m/s^2
In this case, the weight is 10N, then we can write:
10N = M*9.8m/s^2
Solving this for M we get:
10N/(9.8m/s^2) = M = 1.02 kg
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Can I get help? Please show your work and steps.
1) -14 = -4(9x-1)
Number 2
⬇️⬇️⬇️
Answers
Question 1
[tex]-14=-4(9x-1)\\\\-14=-36x+4\\\\-18=-36x\\\\x=\frac{1}{2}[/tex]
Question 2
Multiplying both sides by 12,
[tex]4x-7x=8\\\\-3x=8\\\\x=-\frac{8}{3}[/tex]
Raina and Leila are driving separate cars to Boston. They begin the trip with full gas tanks. The amount of gas (in gallons) remaining in the tank of each car depends on the number of miles driven, as shown below.
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(a) Leila's car, 2 gallons
At 150 miles, Raina's car has 9 gallons of gas and Leila's car had 11 gallons of gas.(b) 300, Raina's car
The amount of gas remaining is when the graphs intersect.Since the graph for Leila's car is higher than the graph for Raina's car before 300 miles, Raina's car will have less gas.(a) Leila's car, 2 gallons At 150 miles, Raina's car has 9 gallons of gas and Leila's car had 11 gallons of gas.
(b) 300, Raina's car The amount of gas remaining is when the graphs intersect.
What's the graph about?(a) At 150 miles, Raina's car has 9 gallons of gas and Leila's car had 11 gallons of gas. This can be seen by looking at the graph of the two cars' gas levels. The graph for Leila's car is higher than the graph for Raina's car at this point, so Leila's car has more gas.
(b) The amount of gas remaining is when the graphs intersect. This happens at 300 miles. Since the graph for Leila's car is higher than the graph for Raina's car before 300 miles, Raina's car will have less gas at this point.
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What is the value of x + y² when x = 1 and y = 9?
Answers
Answer:
=82
Step-by-step explanation:
the value of
x + y²
putting x=1,y=9
we get,
1+(9)^²
=1+81
=82
ASAP i need help rn before i finish this test
The triangles shown are congruent.
What is a correct congruence statement for the triangles shown?
Answers
Answer:
SAS= Side, Angle, Side
Step-by-step explanation:
According to the image, GB congruent to XP, and LB congruent to PF. So, it means that both triangle have the same angle since they both have two congruent side.
Write the equation of the line that is parallel to - 8x-6y = 5 that passes through thepoint (-9, 1)
Answers
First,we will find the slope of the line
Using 8x - 6y = 5
we will have to re-arrange the equation above to be in the slope-intercept form.
That is; it should be in the form y = mx + b
8x - 6y = 5
6y = 8x -5
y = 8/6 x - 5/6
slope = 8/6 = 4/3
In a parellel equation the slope are the same, hence the slope of our new equation is 4/3
Next, we find the intercept of the new equation;
Using the point (-9, 1) and slope(m) = 4/3
we will substitute into the equation below and then solve for b, where b is the slope of our new equation
y = mx + b
1 = 4/3 (-9) + b
1 = 4(-3) + b
1 = - 12 + b
add 12 to both-side of the equation
1+ 12 = b
13 = b
b= 13
Substituting m = 4/3 and b = 13 into the formula; y = mx+ b
y = 4/3 x + 13
[tex]undefined[/tex]Help me! i need this answer now i am so dead. if i get it worng please help
Answers
Answer:
[tex]260 \: {cm}^{2} [/tex]
Step-by-step explanation:
hope it helped, have a nice day!: )
msMario bought 3 yeard of ribbon for 1.50 how much would 5 yards of the same ribbon cost? explain how u got your answer
Answers
For 3 yards, it costs, 1.50.
So for one yard,
[tex]\frac{1.50}{3}=0.5[/tex]Therefore for 5 yards,
[tex]5\times0.5=2.5[/tex]Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Vince is comparing the cost of a fresh lobster dinner at two different restaurants. The first restaurant charges $51 for the meal, plus $5 per kilogram for the lobster he picks. At the second restaurant, Vince would pay $8 per kilogram for the lobster, in addition to $33 for the meal. Vince realizes that, in theory, dinner at both restaurants could cost the same amount if the lobster had a certain weight. How much would Vince pay for his dinner? What is the weight?Dinner would cost $ at either restaurant if Vince's lobster weighed kilograms.
Answers
Based on the given situation, if x is number of kilograms of lobster, you can write the following expressions:
51 + 5x cost in the first restaurant
33 + 8x cost in the second restaurant
In order to determine the value of x which makes the cost the same in both restaurants, equal the previous expressions and solve for x:
51 + 5x = 33 + 8x subtract 33 both sides and 5x subtract both sides
51 - 33 = 8x - 5x simplify
18 = 3x divide by 3 both sides
18/3 = x
6 = x
x = 6
Hence, the weight of the lobster is 6 kg.
The cost of the dinner is:
51 + 5(6) = 51 + 30 = 81
Hence, the cost of the dinner is $81
If a1 = 7 and an3an-1 + 4 then find the value of a4.
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A1 = 7
An = 3A(n-1) + 4. According to this, A2 would be= 3*7 + 4 =25
A1 = 7, A2 = 25, then the difference is d = 18
The general formula for an aritmethic progression is An = A1 + (n -1)d
For A4 = 7 + (4-1)*18 = 61
Hey there Ms or Mr, could you please help me out with this problem? Just a head up, this my homework for today not a quiz. it's about Trapezoids.
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We have to relate the angles of the trapezoid in order to find the measure of BAD.
Given:
[tex]\begin{gathered} AB\mleft\Vert DC\mright? \\ AD\cong BC \end{gathered}[/tex]Then
[tex]\begin{gathered} \angle BAD\cong\angle ABC \\ \angle ADC\cong\angle BCD \end{gathered}[/tex]The angles are congruent because if AD and BC are congruent, and the lines are parallel, they sides will form the same angles.
Also, as the segment AD is "cut" by two parallel lines, the angles BAD and ADC are consecutive interior angles and are, therefore, supplementary.
Then, we can write:
[tex]\begin{gathered} m\angle BAD+m\angle ADC=180\degree\text{ and }\angle ADC=\angle BCD \\ \Rightarrow m\angle BAD+m\angle BCD=180\degree \\ 2x+(3x-5)=180 \\ 5x-5=180 \\ 5x=180+5 \\ 5x=185 \\ x=\frac{185}{5} \\ x=37 \end{gathered}[/tex]Now, with the value of x, we can calculate the measure of BAD as:
[tex]m\angle BAD=2x=2\cdot37=74\degree[/tex]Answer: the measure of BAD is 74°.
Solve for m.m- 15 = 20
Answers
Answer:
m=35
Explanation:
Given the equation:
[tex]m-15=20[/tex]We solve for the value of m by adding 15 to both sides.
[tex]\begin{gathered} m-15+15=20+15 \\ m+0=35 \\ m=35 \end{gathered}[/tex]The value of m is 35.
The result will be m=35
Last year, Carlos opened an investment account $5,200 with. At the end of the year, the amount in the account had increased by 6.5%. How much is this increase in dollars? How much money was in his account at the end of last year?
Answers
ANSWER
[tex]\begin{gathered} 338 \\ 5538 \end{gathered}[/tex]EXPLANATION
The Principal is $5200;
Increase rate is; 6.5%
The increase in dollar is;
[tex]\begin{gathered} \frac{6.5}{100}\times5200 \\ =338 \end{gathered}[/tex]Hence, the amount in the account at the end of the year;
[tex]\begin{gathered} A=P+I \\ =5200+388 \\ =5538 \end{gathered}[/tex]Therefore, the increase in dollar is $338 while the amount in the account at the end of the year is $5538
Select the correct answer. Jonathan has 30 chocolates. He gives some chocolates to his friend David. He then gives Sarah half the number of chocolates that he gave David and gives Lily two-thirds of what he gave David. After giving away the chocolates, Jonathan has 4 chocolates left. If the number of chocolates Jonathan gives David is x, which equation represents the situation? How many solutions does this equation have? A. x + 1 2 x + 2 3 x = 30 − 4 , which has no solution B. x + 1 2 x + 2 3 x = 30 , which has infinitely many solutions C. x + 1 3 x + 2 3 x − 4 = 30 , which has one solution D. x + 1 2 x + 2 3 x + 4 = 30 , which has one solution E. 1 2 x + 2 3 x = x − 4 , which has no solution
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The solution to equation x+ 1/2x+2/3x+4= 30 and has one solution x = 12 which is the correct answer would be an option (D).
The no. of chocolates given to Sarah = 1/2 of x = x/2
Then Lily has two-thirds of what he has given David. Following the distribution of the chocolates,
The number of chocolates provided to Lily is equal to two-thirds of the number of chocolates given to David.
The number of chocolates given to Lily Equals 2/3 of x = 2x/3
Now, the total number of chocolates delivered to David, Sarah, and Lily
= x+x/2+2x/3
Here LCM of 2 and 3 is 6
The Total no. of chocolates given to David, Sarah, and lily
= (6x + 3x+ 4x)/6
The total number of chocolates distributed to David, Sarah, and Lily is 13x/6.
Jonathan had four chocolates left after giving them out.
The number of chocolates left with Jonathan equals the total number of chocolates given to David, Sarah, and Lily.
⇒ 4 = 30 - 13x/6
⇒ 4 + 13x/6 = 30
⇒ 13x/6 = 30-4 = 26
⇒ x = 26×6/13 = 2×6
⇒ x = 12
Hence, the equation which represents the given situation is 30 - 13x/6 =4
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I need help with this question but no one is helping me! Can someone please help me
Answers
Answer:
a) 0.0187
b) 0.0943
c) 0.2959
Step-by-step explanation:
a) 9/31 * 8/30 * 7/29 = 0.0187
b) 10/31 * 9/30 * 8/29 + 12/31 * 11/30 * 10/29 + 9/31 * 8/30 * 7/29 = 0.0943
c) 21/31 * 20/30 * 19/29 = 0.2959
What is a(b(x)) if a(x) = 3x 2 and g(x) = -3x + 1?
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The equivalent composite function is expressed as -9x + 5
Composite functionsComposite functions are also known as function of a function.
Given the following functions:
a(x) = 3x+2 and
b(x) = -3x + 1
Determine the value of a(b(x))
a(b(x)) = a(-3x+1)
a(b(x)) = 3(-3x+1) + 2
a(b(x)) = -9x + 3 + 2
a(b(x)) = -9x + 5
This gives the equivalent composite function.
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I'll give brainliest!!
Answers
2. Y of the power of 4
3.Y of the power of 9
4.Y of the power of 6
negative 37 over 24 times j minus 17 over 12
negative 37 over 24 times j plus 17 over 12
43 over 24 times j plus 1 over 12
negative 43 over 24 times j plus negative 1 over 12
Simplify the expression.
the expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths
negative 37 over 24 times j minus 17 over 12
negative 37 over 24 times j plus 17 over 12
43 over 24 times j plus 1 over 12
negative 43 over 24 times j plus negative 1 over 12
Which expression is equivalent to 3(−4.5b − 2.1) − (6b + 0.6)?
19.5b + 1.5
−19.5b − 1.5
−19.5b − 6.9
19.5b − 6.9
Answers
The Simplification of the expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths is "negative 43 over 24 times j plus negative 1 over 12". option D
The expression which is equivalent to 3(−4.5b − 2.1) − (6b + 0.6) is −19.5b − 6.9. option c
Simplification of fractionnegative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths
= -1/8j + 2/3 - (5/3j + 9/12)
= -1/8j + 2/3 - 5/3j - 9/12
= -1/8j - 5/3j + (2/3 - 9/12)
= (-3j-40j / 24 + (8-9) / 12
= -43/24j + (-1)/12
The expression equivalent to 3(−4.5b − 2.1) − (6b + 0.6)
open parenthesis= -13.5b - 6.3 - 6b - 0.6
collect like terms= -13.5b - 6b - 6.3 - 0.6
= - 19.5b - 6.9
So therefore, the equivalent expression to 3(−4.5b − 2.1) − (6b + 0.6) is - 19.5b - 6.9
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h(x)=−2x+2
Find h(−2).
Answers
Answer:
6
Step-by-step explanation:
when you change h[×] to h[-2] , -2x +2 change to -2[-2]+2
which graph represents the systems of inequalities? there are 4 graphs for this question total please help
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Looking at the inequalities, it involves the 'less than or equal to' symbol. This means that the lines of both inequalities must be solid. In options B, C and D, one or two of the lines is broken. This is an indication that they don't represent the given inequality. We would check option A
Optiona
|-102.06|
Find the absolute value
Answers
Answer:
102.06
Step-by-step explanation:
Absolute values are always positive
Answer:
Step-by-step explanation:
102.06
Absolute value is just the positive of any value.
Hope this helps! Have a nice day!
#8.Verify algebraically if the function is even, odd, or neither
Answers
g(x)= x^4 √(1+x)
g(-x) = (-x)^4 √1-x
g (-x) = x^4 √1-x
Since the obtained function is not the same or the opposite it is neither.
a. On what interval(s) of x is f(x) positive?
b. On what interval(s) of x is f(x) negative?
c. On what interval(s) of x is f(x) increasing?
d. On what interval(s) of x is f(x) decreasing?
e. On what interval(s) of x does f have positive concavity?
f. On what interval(s) of x does f have negative concavity?
Answers
On (-∞, -2) ∪ (3,∞) f(x) is positive, On (-∞, -0.5) it is negative, On (0.5, ∞) it is increasing, in none of the intervals it is having positive concavity, On (-∞, ∞) it has negative concavity.
What X intervals are beneficial for fx?Seeing as how f (x) = 0 there. A function’s “positive regions” are those times when it is above the x-axis. Y-values that are positive are where it is (not zero).
The portions of a function that are below the x-axis are known as its negative regions.
How can I determine the time intervals where f is positive?You must first take the derivative, then make it equal to 0, and then determine which zero values the function is positive between in order to determine when a function is rising. In order to determine when the function is positive and, thus, rising, test values on all sides of these.
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What is the equation of the line that passes through the point (4,-8) and has a slope of −2
Answers
Answer:
See below
Step-by-step explanation:
Point (4,-8) slope form would be
( y - -8) = -2 ( x -4)
y+8 = -2x + 8 re-arrange to y = mx + b form
y = - 2x
A traffic study has shown that the probability that 5 cars will pass over a small bridge in a 4-minute period is 0.16.What are the odds against exactly 5 cars passing over the bridge in that time?
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A probability is the number of outcomes divided by the number of total outcomes.
An odd is given by a:b, in which a is the number of successes and b is the number of failures.
From the question, the probability of 5 cars will pass over a small bridge is 0.16
That means the total outcomes is 100 and the outcomes of successes are 16
Then to find the failures subtract 16 from 100
The failures = 100 - 16 = 84
Successes = 16
a = 16
Failures = 84
b = 84
Odds = a: b
Odds = 16: 84
Divide each term by 4 to simplify
Odds = (16/4): (84/4)
Odds = 4: 21
The answer is 4: 21