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 + 5xB) y = -x^2 + 4x - 4C) y = -2x^2 +4x - 4D) y = -2.25x^2 + 4.5x - 2

Answer:   C)  y = -2x^2 +4x - 4Step-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 solutionIf 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 -4Filling 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 = -16Adding 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 -2The equation that fits the given data is ...   y = -2x² +4x -4