Question

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

Answer 1

Simplified equation in standard form:
`y=(1)/(4)x^(2)+12(1)/(4)`

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

Explanation:

`y=(1)/(2)(x+3)^2+10`

Step 1: Distribute the
`(1)/(2)` :

`y=((1)/(2)*x+(1)/(2)*3)^2+10`

`y=((1)/(2)x+1(1)/(2))^2+10`

Step 2: Take
`((1)/(2)x+1(1)/(2))` and square it :

`y=((1)/(2)x+1(1)/(2))^2+10`

`y=((1)/(2)x)^(2) +(1(1)/(2))^2+10`

`y=((1)/(2)x*(1)/(2)x)+(1(1)/(2)*1(1)/(2))+10`

`y=(1)/(4)x^(2)+2(1)/(4)+10`

Step 3: Add the constants:

`y=(1)/(4)x^(2)+(2(1)/(4)+10)`

`y=(1)/(4)x^(2)+(12(1)/(4))`

Step 4: Get rid of the parenthesis:

`y=(1)/(4)x^(2)+12(1)/(4)`