Answer:
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