Question

The parabola opens upward has x = 2 as an axis of symmetry and contains the non -vertex points (1, 9) and (4, 27) write the equation in vertex form for this parabola .

Answer 1

f(x) = 6(x - 2)² + 3

Explanation:

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

"the parabola opens upward" means: a>0

"the parabola has x = 2 as an axis of symmetry" means: h = 2

so f(x) = a(x - 2)² + k

"the parabola contains the point (1, 9)" means:

9 = a(1 - 2)² + k

9 = a(-1)² + k

9 = a + k

k = 9 - a

"the parabola contains the point (4, 27)" means:

27 = a(4 - 2)² + k

so:

27 = a(2)² + 9 - a

27 = 4a + 9 - a

3a = 18

a = 6

and k = 9 - 6 = 3

Therefore the vertex form for this parabola is:

f(x) = 6(x - 2)² + 3