What is $y=2(x+3)^2+1$ in standard form?

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Answer 1 · 2016-03-01T23:01:41

$y=2(x+3)^2+1$ in standard form is $color(purple)(y=2x^2+12x+19)$ .

$y=2(x+3)^2+1$ is a quadratic equation in vertex form. It can be converted into standard form by doing the following:

Remove the parentheses and exponent by simplifying $(x+3)^2$ , which is a sum of squares.

$a^2+b^2=a^2+2ab+b^2$ , where $a=x, and b=3$ .

$color(blue)((x+3)^2=x^2+2*x*3+3^2)$

Simplify.

$color(blue)((x^2+6x+9)$

Rewrite the equation, substituting $color(blue)((x^2+6x+9))$ for $(x+3)^2$ .

$y=2color(blue)((x^2+6x+9))+1$

Distribute the $color(red)2$ .

$y=color(red)2*x^2+6x*color(red)2+9*color(red)2+1$

Simplify.

$y=color(purple)(2x^2+12x+18)+1$

Simplify.

$color(purple)(y=2x^2+12x+19)$

What is y=2(x+3)^2+1y=2(x+3)^2+1 in standard form?