Answer:
C) y = -2x^2 +4x - 4
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
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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