Question

Write the quadratic function represented by the graph.

Answer 1

( -2, 0 )

( 2, 32 )

( 4, 0 )

Explanation:

not so sure tho

Answer 2

The quadratic function represented by the given graph is
`y = -4x^2 + 8x + 32.`

The quadratic function represented by the given graph can be determined by finding its equation in the form of
`y = ax^2 + bx + c`, where a, b, and c are constants.

To find the equation, we can use the points (-2, 0), (2, 32), and (4, 0) that are on the graph.

Step 1: Substitute the coordinates of the points into the equation
`y = ax^2 + bx + c.`
Using the point (-2, 0):

`0 = a(-2)^2 + b(-2) + c`

Using the point (2, 32):

`32 = a(2)^2 + b(2) + c`

Using the point (4, 0):

`0 = a(4)^2 + b(4) + c`

Step 2: Solve the resulting system of equations to find the values of a, b, and c.

From the equation
`0 = a(-2)^2 + b(-2) + c,`we get:
4a - 2b + c = 0 ------ (1)

From the equation
`32 = a(2)^2 + b(2) + c`, we get:
4a + 2b + c = 32 ------ (2)

From the equation
`0 = a(4)^2 + b(4) + c`, we get:
16a + 4b + c = 0 ------ (3)

Step 3: Solve the system of equations (1), (2), and (3).

Subtracting equation (1) from equation (2), we get:
4a + 2b + c - (4a - 2b + c) = 32 - 0
4b = 32
b = 8

Substituting b = 8 into equation (1), we get:
4a - 2(8) + c = 0
4a - 16 + c = 0
4a + c = 16
c = 16 - 4a

Substituting b = 8 and c = 16 - 4a into equation (3), we get:
16a + 4(8) + (16 - 4a) = 0
16a + 32 + 16 - 4a = 0
12a + 48 = 0
12a = -48
a = -4

Step 4: Substitute the values of a, b, and c back into the equation y = ax^2 + bx + c.

Therefore, the quadratic function represented by the graph is:


`y = -4x^2 + 8x + (16 - 4(-4))`

`y = -4x^2 + 8x + 32`.