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

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Answer 1 · 2016-03-01T23:01:41

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

$y = 2 {(x + 3)}^{2} + 1$ $y=2(x+3)^2+1$ 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 ${(x + 3)}^{2}$ $(x+3)^2$ , which is a sum of squares.

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

${(x + 3)}^{2} = x^{2} + 2 \cdot x \cdot 3 + 3^{2}$ $color(blue)((x+3)^2=x^2+2*x*3+3^2)$

Simplify.

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

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

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

Distribute the $2$ $color(red)2$ .

$y = 2 \cdot x^{2} + 6 x \cdot 2 + 9 \cdot 2 + 1$ $y=color(red)2*x^2+6x*color(red)2+9*color(red)2+1$

Simplify.

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

Simplify.

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

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