Question

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?

Answer 1

f(x) = a(x-h)² + k

Given that the vertex is (-3 -6):

f(x) = a(x + 3)² -6

Given that it passes through (0.0), find a:

a(0 + 3)² - 6 = 0

9a - 6 = 0

9a = 6

a = 6/9 =2/3

So the equation is :

f(x) = 2/3(x + 3)² -6

Write the equation in standard form:

f(x) = 2/3(x² + 6x + 9) - 6

f(x) = 2/3x² + 4x + 6 - 6

f(x) = 2/3x² + 4x

Answer: f(x) = 2/3x² + 4x