Question

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

Answer 1

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            -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