Question

How do you find the quadratic function with vertex (-2,5) and point (0,9)?

Answer 1

Answer: y = (x +2)² + 5

Step-by-step explanation:

y = a(x - h)² + k where "a" is the leading coefficient and (h, k) is the vertex

Since we don't know "a", we need to plug in the point (x, y) and the vertex (h, k) to solve for "a":  (x, y) = (0, 9) and (h, k) = (-2, 5)

y = a(x - h)² + k

9 = a(0 - (-2))² + 5

9 = a(0 + 2)² + 5

9 = a(2)² + 5

-5            -5

4  =  a(4)

÷4   ÷4  

 1 = a

Next, plug in "a" and the vertex (h, k):

y = a(x - h)² + k

y = 1(x +2)² + 5

y = (x +2)² + 5