What is the equation, in standard form, of a parabola that contains the following points?

(-2, -20), (0, -4), (4, -20)

a) y = -2.5x^2 + 5x
b) y = -x^2 + 4x - 4
c) y = -2x^2 +4x - 4
d) y = -2.25x^2 + 4.5x - 2

  C)  y = -2x^2 +4x - 4

Step-by-step explanation:

The y-values are the same for points (-2, -20) and (4, -20), so the axis of symmetry is halfway between those points, at x = (-2+4)/2 = 1.

The y-intercept is (0, -4), so the only viable answer choices are B and C. The axis of symmetry is given by ...

  x = -b/(2a)

For choice B, this is x = -4/(2(-1)) = 2 (doesn't work).

For choice C, this is x = -4/(2(-2)) = 1, which matches the above analysis.

The appropriate choice is ...

  y = -2x^2 +4x - 4

_____

Alternate solution

If you like, you can derive the equation for the parabola. Since you know that the y-intercept is -4, you can write the equation as ...

  y = ax² +bx -4

Filling in the data points that are not x=0, we have two equations in two unknowns:

  -20 = a(-2)² +b(-2) -4   ⇒   4a -2b = -16

  -20 = a(4)² + b(4) -4    ⇒   16a +4b = -16

Adding twice the first equation to the second gives ...

  2(4a -2b) + (16a +4b) = 2(-16) +(-16)

  24a = -48

  a = -2 . . . . . . . . matches choice C

  4(-2) -2b = -16 . . . . . substitute into an equation to find b

  -2b = -8 . . . . . . . . . . add 8

  b = 4 . . . . . . . . . . . . . divide by -2

The equation that fits the given data is ...

  y = -2x² +4x -4