Question

Write the equation of the parabola in vertex form that has the following properties: passes through the point (2, 12) and has a vertex of (4,-4)​

Answer 1

f(x) = 4(x - 4)² - 4

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 (4, -4) is

f(x) = a(x - 4)² - 4

passes through the point (2, 12) means if x=2 then f(x)=12

12 = a(2 - 4)² - 4

12 +4 = a(-2)² - 4 +4

16 = 4a

a = 4

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

f(x) = 4(x - 4)² - 4