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

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

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`