Question

Write an equation of the parabola in vertex form.

Answer 1

y = (x - 4)² - 9

Explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

here (h, k ) = (4, - 9 ) , then

y = a(x - 4)² - 9

to find a substitute the coordinates of any other point on the graph into the equation.

using the point (8, 7 )

7 = a(8 - 4)² - 9 ( add 9 to both sides )

16 = a(4)² = 16a ( divide both sides by 16 )

1 = a

Then

y = (x - 4)² - 9 ← equation of parabola in vertex form