Question

PLEASE HELP!!!!

Fit a Quadratic function to these three points:
(-2,8), (0,-4) and (4,68)

A. y=4x^2+2x-4

B. y=-2x^+2x-4

C. y=-4x^2-2x-4

D. y=-2x^2-2x-4

Answer 1

One way to find this is to plug in the points into each of the answers and see which one is correct:

A. First, plug in the point (-2,8). y = 8, x = -2

`y = 4 {x}^(2) + 2x - 4 \\ (8) = 4 {( - 2)}^(2) + 2( - 2) - 4 \\ 8 = 16 - 4 - 4 \\ 8 = 8`
A works for the first point.
Then plug in the second point: x =0, y = -4

`( - 4) = 4 {(0)}^(2) + 2(0) - 4 \\ - 4 = - 4`
A works for the second point.
Then plug in the third point: x = 4, y = 68

`(68) = 4 {(4)}^(2) + 2(4) - 4 \\ 68 = 64 + 8 - 4 \\ 68 = 68`
A works for the third point, so A is the answer.

But we should double-check the other answers too.


`y = - 2 {x}^(2) + 2x - 4`

`(8) = - 2( { - 2)}^(2) + 2( - 2) - 4 \\ 8 = - 8 - 4 - 4 \\ 8 = - 16`
B does not work.


`y = - 4 {x}^(2) - 2x - 4 \\ (8) = - 4 {( - 2)}^(2) - 2( - 2) - 4 \\ 8 = - 16 + 4 - 4 \\ 8 = - 16`
C does not work.


`y = - 2 {x}^(2) - 2x - 4 \\ (8) = - 2 {( - 2)}^(2) - 2( - 2) - 4 \\ 8 = - 8 + 4 - 4 \\ 8 = - 8`
D does not work.

Therefore, A is the answer