Question

The minimum of the graph of a quadratic function is located at (–1, 2). The point (2, 20) is also on the parabola. Which function represents the situation?

f(x) = (x + 1)2 + 2
f(x) = (x – 1)2 + 2
f(x) = 2(x + 1)2 + 2
f(x) = 2(x – 1)2 + 2

Answer 1

Use vertex form f(x)=a(x−h)^2+k with vertex (h,k)=(-1,2): f(x)=a(x+1)^2+2.
Plug in (2,20): 20 = a(2+1)^2 + 2 = 9a + 2 → 9a = 18 → a = 2.

So f(x) = 2(x + 1)^2 + 2.