Answer:
y = (x + 4)² - 6
Step-by-step explanation:
the equation of a quadratic function in vertex form is
f(x) = a(x - h)² + k
(h, k ) are the coordinates of the vertex and a is a multiplier
From the graph
vertex = (- 4, - 6 ) , then
f(x) = a(x - (- 4) )² - 6, that is
f(x) = a(x + 4)² - 6
To find a, substitute the coordinates of any other point on the graph into f(x)
using the point on the graph ( - 2, - 2 )
- 2 = a(- 2 + 4)² - 6 ( add 6 to both sides )
4 = a(2)² = 4a ( divide both sides by 4 )
1 = a
f(x) = (x + 4)² - 6
