Answer:
f(x) = 6(x - 2)² + 3
Step-by-step 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
