Answer:
f(x) = 2(x - 1)² + 2
Explanation:
The vertex form is f(x) = a(x - h)² + k, where the vertex is (h, k).
Putting in the given vertex, we get f(x) = a(x - 1)² + 2. To find a, we put in the other point that the parabola passes through (4, 20) which is [x, f(x)].
20 = a(4 - 1)² + 2
20 = a(3)² + 2
20 = 9a + 2 (subtract 2 from both sides to get a alone)
-2 -2
18 = 9a (divide both sides by 9 to get a by itself)
9 9
2 = a (put that into our vertex form equation)
f(x) = 2(x - 1)² + 2