Question

The graph of function g is a parabola with the vertex located at (5, 9). The parabola also passes through the point (3, 1). Which of the following is an equation in vertex form for this function?

a) g(x) = 2(x - 5)² + 9
b) g(x) = 2(x - 5)² - 9
c) g(x) = 2(x - 5)² + 9
d) g(x) = 2(x + 5)² + 9

Answer 1

The equation of the described parabola:

y = -2*(x - 5)² + 9

How to find the equation of the parabola?

We know that a quadratic equation with a vertex in (h, k) and a leading coefficient a can be written as:

y = a*(x - h)² + k

Here we know that the vertex is at (5, 9), then:

y = a*(x - 5)² + 9

And the parabola passes through (3, 1), then:

1 = a*(3 - 5)² + 9

1 = a*4 + 9

1 - 9 = 4a

-8/4 = a

-2 = a

The equation is:

y = -2*(x - 5)² + 9