Question

Quadratic function with (-2,4) as the vertex and passes through (-4,-4)

Answer 1

-2x^2 + 8 because if you turn it into vertex form and determine

Answer 2

Answer:

$f(x)=-2x^2-8x-4$

Step-by-step explanation:

Vertex form of quadratic function:  $f(x)=a(x-h)^2+k$

where $(h,k)$ is the vertex

Given:

• vertex = (-2, 4)

$\implies f(x)=a(x+2)^2+4$

Given:

• point on curve = (-4, -4)

$\implies f(-4)=-4\\\\\implies a(-4+2)^2+4=-4\\\\\implies a(-2)^2=-4-4\\\\\implies 4a=-8\\\\\implies a = -2$

Therefore,

$f(x)=-2(x+2)^2+4\\\\\implies f(x)=-2(x^2+4x+4)+4\\\\\implies f(x)=-2x^2-8x-8+4\\\\\implies f(x)=-2x^2-8x-4$