given the vertext (-2,-7) and the y-intercept -3 determine the quadratic formula

Question

must determine the quadratic function f whose graph is given

Answer 1

f(x) = a(x - h)² + k

f(x) = a(x + 2)² - 7

 

(0,-3)

-3 = a(0 + 2)² - 7

4 = a(2)²

4 = 4

1 = a

f(x) = 1(x + 2)² - 7 = x² + 4x - 3

 

 

Answer 2

Since the vertex is  (-2,-7)

 

The vertex form of the quadratic function is:

 f(x)  =  a (x+2)² -7  for some value of a.

 

The y intercept is -3   means f(0) = -3   so

 

-3 =  a( 0 +2)²  -7       solving for a gives  a = 1

 

Final answer f(x) = (x + 2)²  -7   =   x² + 4 x -3