## Write an equation in vertex form of the parabola that passes through (4, 20) and has a vertex of (1, 2). *

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## Answers ( )

Answer:f(x) = 2(x – 1)² + 2

Step-by-step 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 -218 = 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