Question

What is y=1/2(x+3)^2+10 in standard form​

Answer 1

Answer:

Simplified equation in standard form: $y=\frac{1}{4}x^{2}+12\frac{1}{4}$

Original equation in standard form: $y=1/2(x+3)^2+10$

Step-by-step explanation:

$y=\frac{1}{2}(x+3)^2+10$

Step 1: Distribute the $\frac{1}{2}$ :

$y=(\frac{1}{2}*x+\frac{1}{2}*3)^2+10$

$y=(\frac{1}{2}x+1\frac{1}{2})^2+10$

Step 2: Take $(\frac{1}{2}x+1\frac{1}{2})$ and square it :

$y=(\frac{1}{2}x+1\frac{1}{2})^2+10$

$y=(\frac{1}{2}x)^{2} +(1\frac{1}{2})^2+10$

$y=(\frac{1}{2}x*\frac{1}{2}x)+(1\frac{1}{2}*1\frac{1}{2})+10$

$y=\frac{1}{4}x^{2}+2\frac{1}{4}+10$

Step 3: Add the constants:

$y=\frac{1}{4}x^{2}+(2\frac{1}{4}+10)$

$y=\frac{1}{4}x^{2}+(12\frac{1}{4})$

Step 4: Get rid of the parenthesis:

$y=\frac{1}{4}x^{2}+12\frac{1}{4}$