Question

What is the equation written in vertex form of a parabola with a vertex of (3,6) that passes

through point (4,4)?

Answer 1

f(x) = -2(x - 3)² + 6

Explanation:

The vertex form of an equation of the parabola:

f(x) = a(x - h)² + k

the vertex is (3, 6) ⇒ h = 3, k = 6

so:

f(x) = a(x - 3)² + 6

The parabola goes through the point (4, 4) ⇒ x=4, f(x)=4

4 = a(4 - 3)² + 6

4 = a(1)² + 6

-6 -6

- 2 = a

It means the equation of the parabola in vertex form:

f(x) = -2(x - 3)² + 6