Question

Converting from vertex form to standard form 2%29%20%7B%7D%5E%7B2%7D%20%20-%204" id="TexFormula1" title="y = \frac{1}{2} (x - 2) {}^{2} - 4" alt="y = \frac{1}{2} (x - 2) {}^{2} - 4" align="absmiddle" class="latex-formula">
​

Answer 1

Answer:

$\displaystyle f(x)=\frac{1}{2}x^2-2x-2$

Step-by-step explanation:

To convert from vertex form to standard form, we can simply expand.

So, we have:

$\displaystyle f(x)=\frac{1}{2}(x-2)^2-4$

Expand the square:

$\displaystyle f(x)=\frac{1}{2}(x^2-4x+4)-4$

Distribute:

$\displaystyle f(x)=\frac{1}{2}x^2-2x+2-4$

Simplify:

$\displaystyle f(x)=\frac{1}{2}x^2-2x-2$