Answer:
Simplified equation in standard form: [tex]y=\frac{1}{4}x^{2}+12\frac{1}{4}[/tex]
Original equation in standard form: [tex]y=1/2(x+3)^2+10[/tex]
Step-by-step explanation:
[tex]y=\frac{1}{2}(x+3)^2+10[/tex]
Step 1: Distribute the [tex]\frac{1}{2}[/tex] :
[tex]y=(\frac{1}{2}*x+\frac{1}{2}*3)^2+10[/tex]
[tex]y=(\frac{1}{2}x+1\frac{1}{2})^2+10[/tex]
Step 2: Take [tex](\frac{1}{2}x+1\frac{1}{2})[/tex] and square it :
[tex]y=(\frac{1}{2}x+1\frac{1}{2})^2+10[/tex]
[tex]y=(\frac{1}{2}x)^{2} +(1\frac{1}{2})^2+10[/tex]
[tex]y=(\frac{1}{2}x*\frac{1}{2}x)+(1\frac{1}{2}*1\frac{1}{2})+10[/tex]
[tex]y=\frac{1}{4}x^{2}+2\frac{1}{4}+10[/tex]
Step 3: Add the constants:
[tex]y=\frac{1}{4}x^{2}+(2\frac{1}{4}+10)[/tex]
[tex]y=\frac{1}{4}x^{2}+(12\frac{1}{4})[/tex]
Step 4: Get rid of the parenthesis:
[tex]y=\frac{1}{4}x^{2}+12\frac{1}{4}[/tex]
