1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Shtirlitz [24]
3 years ago
9

This graph represents a quadratic function. What is the function’s equation written in factored form and in vertex form?

Mathematics
1 answer:
creativ13 [48]3 years ago
4 0

Answer:

Part a) The function’s equation written in vertex form is

f(x)=2(x-2)^2-8

Part b) The function’s equation written in factored form is equal to

f(x)=2x(x-4)

Step-by-step explanation:

Part a) What is the function’s equation written in vertex form?

we know that

The equation of a vertical parabola written in vertex form is equal to

f(x)=a(x-h)^2+k

where

a is a coefficient

(h,k) is the vertex

Looking at the graph

The vertex is the point (2,-8)

substitute

f(x)=a(x-2)^2-8

Find the value of the coefficient a

take one point from the graph

(0,0)

substitute in the equation

0=a(0-2)^2-8\\0=4a-8\\4a=8\\a=2

therefore

The function’s equation written in vertex form is

f(x)=2(x-2)^2-8

Part b) What is the function’s equation written in factored form?

we know that

The equation of a vertical parabola written in factored form is equal to

f(x)=a(x-x_1)(x-x_2)

where

a is a coefficient

x_1 and x_2 are the zeros or x-intercepts of the function

Remember that the x-intercept is the value of x when the value of the function is equal to zero

Looking at the graph

The zeros or x-intercepts of the function are

x=0 and x=4

so

f(x)=a(x-0)(x-4)

f(x)=ax(x-4)

Find the value of the coefficient a

take one point from the graph

(2,-8)

substitute

-8=a(2)(2-4)\\-8=-4a\\a=2

therefore

The function’s equation written in factored form is equal to

f(x)=2x(x-4)

You might be interested in
PLSSS HELP ME!!!!!!!!!!! I WILL MARK U!!!!!
max2010maxim [7]

Answer:

a2

Step-by-step explanation:

you're using the pythagorean theorem

8 0
3 years ago
What is the rule for finding the distance of a point when the points are in the same Quadrant?
s344n2d4d5 [400]
Find the horizontal and vertical distance between the points. First, subtract y2 - y1 to find the vertical distance. Then, subtract x2 - x1 to find the horizontal distance.
6 0
3 years ago
The height of a cone-shaped statue is 9 ft, and the diameter is 12 ft.
Pepsi [2]
I hope this helps you



Volume of cone =1/3.pi.r^2.h



Volume of cone =1/3.3,14.6^2.9



Volume of cone =339.12
3 0
3 years ago
Read 2 more answers
Simplify 3^2 x 3^3 <br><br> A. 3<br><br> B. 3^6<br><br> C. 3^5<br><br> D. 3^8
Maslowich
When you are multiplying and have like bases, then you add the exponents. 
2+3=5
3^5
5 0
2 years ago
PR = 9x - 31 and QR = 43; find x
lesya692 [45]
PR=9(43)-31

PR=387-31

PR=356

I think that's the answer :)
3 0
3 years ago
Other questions:
  • A restaurant manager needs to rope off a rectangular section for a private party. The length of the section must be 7.4 m. The m
    9·1 answer
  • HELPPP PLEASE!!!! SHOW ALL WORK!!!
    5·2 answers
  • Find the roots of the equation below. 7x2 + 3 = 8x
    7·2 answers
  • What is the answer?
    15·1 answer
  • Convert 14x + 6y = 36 to Y intercept form.
    15·2 answers
  • Could someone please explain this to me? Would be greatly appreciated <br> Work out: 4/5 - 2/3
    8·1 answer
  • In an orchard, there are 13 apple trees, 25 orange trees, and a cherry tree. What is the ratio of orange trees to cherry trees?​
    9·1 answer
  • Write in words what you do to make x the subject of the formula x^2 + y^2 = z^2 .<br> Please explain
    7·1 answer
  • PLEASE HELP! WILL MARK AND GIVE POINTS.
    15·1 answer
  • First, and correct answer gets brainliest, also worth 50 points
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!