Question

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

Answer 1

Answer:

            f(x) = -2(x - 3)² + 6

Step-by-step 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