#### Question

f(x) is a quadratic function whose graph has a vertex at the point (-3 , 2) and has a y-intercept at the point (0 , -16).

Find the equation for function f(x).

Find the x-intercepts of the graph of f(x).

Question

Find the equation for function f(x).

Find the x-intercepts of the graph of f(x).

Since the vertex of the quadratic function is at the point (-3 , 2),

The equation for function is

f(x)=a(x+3)^2+2

Since the function has a y-intercept at the point (0 , -16), we get the following equation

-16 = a(0+3)^2+2

Solve the equation

a = -2

Therefore, the equation for quadratic function is

f(x)=-2(x+3)^2+2

If f(x) = 0,

-2(x+3)^2+2 = 0

(x+3)^2=1

x+3=\pm 1

x=-2 and x=-4

Therefore, the x-intercepts of the graph of f(x) are points (-4,0) and (-2,0)