Question

If the point (0, 20) is the y-intercept of the parabola with the vertex is (8, -12), What is the equation for this parabola.

Answer 1

f(x) = ¹/₂(x - 8)² - 12

Explanation:

f(x) = a(x - h)² + k - vertex form of the equation of the parabola with vertex (h, k)

so the equation of parabola with the vertex (8, -12) is

f(x) = a(x - 8)² - 12

The point (0, 20) is the y-intercept means if x=0 then f(x)=20

20 = a(0 - 8)² - 12

20 +12 = 64a - 12 +12

32 = 64a

a = ³²/₆₄ = ¹/₂

Therefore the equation (in vertex form) of parabla is:

f(x) = ¹/₂(x - 8)² - 12