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
[tex]y = 4 {x}^{2} + 2x - 4 \\ (8) = 4 {( - 2)}^{2} + 2( - 2) - 4 \\ 8 = 16 - 4 - 4 \\ 8 = 8[/tex]
A works for the first point.
Then plug in the second point: x =0, y = -4
[tex]( - 4) = 4 {(0)}^{2} + 2(0) - 4 \\ - 4 = - 4[/tex]
A works for the second point.
Then plug in the third point: x = 4, y = 68
[tex](68) = 4 {(4)}^{2} + 2(4) - 4 \\ 68 = 64 + 8 - 4 \\ 68 = 68[/tex]
A works for the third point, so A is the answer.
But we should double-check the other answers too.
[tex]y = - 2 {x}^{2} + 2x - 4[/tex]
[tex](8) = - 2( { - 2)}^{2} + 2( - 2) - 4 \\ 8 = - 8 - 4 - 4 \\ 8 = - 16[/tex]
B does not work.
[tex]y = - 4 {x}^{2} - 2x - 4 \\ (8) = - 4 {( - 2)}^{2} - 2( - 2) - 4 \\ 8 = - 16 + 4 - 4 \\ 8 = - 16[/tex]
C does not work.
[tex]y = - 2 {x}^{2} - 2x - 4 \\ (8) = - 2 {( - 2)}^{2} - 2( - 2) - 4 \\ 8 = - 8 + 4 - 4 \\ 8 = - 8[/tex]
D does not work.
Therefore, A is the answer
