Question

Rewrite the quadratic function in standard form.h(x) = 2x^2 + 8x − 4h(x) = Give the vertex.(x, y) =

Answer 1

Given the following equation of a quadratic function:

$h(x)=2x^2+8x−4$

We will rewrite the quadratic function in standard form.

The general standard form will be as follows:

$h(x)=a(x+h)^2+k$

So, we will make a complete square for the given function as follows:

$\begin{gathered} h(x)=2x^2+8x−4 \\ h(x)=2(x^2+4x)-4 \\ h(x)=2(x^2+4x+4-4)-4 \\ h(x)=2(x^2+4x+4)-2*4-4 \\ \\ h\mleft(x\mright)=2\left(x+2\right)^2-12 \end{gathered}$

Comparing the last result to the general form:

h = -2, k = -12

So, the answer will be:

$h(x)=2(x+2)^{2}-12$

The vertex = (x,y) = (-2, -12)