Find the equation, f(x) = a(x-h)2 + k, for a parabola that passes through the point (0, 0) and has (-3, -6) as its vertex. What is the standard form of the equation?

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Answered on Tue May 24 2022

The vertex is at (-3, -6) so the vertex form is

y = a(x - (-3))^2 - 6

y = a(x + 3)^2 - 6

Now we find the value of a by substituting x = 0 and y = 0:

0 = a(0 + 3)^2 - 6

9a = 6

a = 2/3.

Vertex form is y = 2/3(x + 3)^2 - 6.

Convert to Standard form:

Multiply through by 3:

3y = 2(x + 3)^2 - 18

3y = 2x^2 + 12x + 18 - 18

3y = 2x^2 + 12x

y = 2/3x^2 + 4x.