Answer:
[tex]f(x)=-2x^2-8x-4[/tex]
Step-by-step explanation:
Vertex form of quadratic function: [tex]f(x)=a(x-h)^2+k[/tex]
where [tex](h,k)[/tex] is the vertex
Given:
[tex]\implies f(x)=a(x+2)^2+4[/tex]
Given:
- point on curve = (-4, -4)
[tex]\implies f(-4)=-4\\\\\implies a(-4+2)^2+4=-4\\\\\implies a(-2)^2=-4-4\\\\\implies 4a=-8\\\\\implies a = -2[/tex]
Therefore,
[tex]f(x)=-2(x+2)^2+4\\\\\implies f(x)=-2(x^2+4x+4)+4\\\\\implies f(x)=-2x^2-8x-8+4\\\\\implies f(x)=-2x^2-8x-4[/tex]
