What is the equation, in standard form, of a parabola that contains the following points (-2,-16),(0,-4), (4,-28) a.y=2x^2-2x-4 b. y=4x^2 + 2x +2 c. y= -2x^2 + 2x -4 d. y= 2x^2 - 2x + 4

Question

whpalmer4 · Answer

A parabola has an equation which can be written in the form $$y = ax^2+bx+c$$We have 3 known points, and 3 unknown variables.  It must be our lucky day, because 3 points will allow us to find all 3 unknown variables!

Our points are: $(-2,-16),\,(0,-4),\,(4,-28)$

We can substitute each point into the equation to find a different equation in terms of $a,b,c$:

$$-16 = a(-2)^2 + b(-2) + c$$$$-4 =a(0)^2 + b(0) + c$$$$-28=a(4)^2 + b(4) + c$$

Simplify and solve that system of equations to get the coefficients for your parabola equation.