Aryan Phillips

2022-02-03

What is the standard form of $y=2{\left(x+4\right)}^{2}-21$?

anthonystb5

Explanation:
Standard quadratic form is $y=a{x}^{2}+bx+c$.
$y=2{\left(x+4\right)}^{2}-21$
First, simplify the expression in the parenthesis with exponent:
y=2(x+4)(x+4)-21
$y=2\left({x}^{2}+8x+16\right)-21$
$y=2{x}^{2}+16x+32-21$
$y=2{x}^{2}+16x+11$
As you can see, this is now in the form $y=a{x}^{2}+bx+c$.
Result:
$y=2{x}^{2}+16x+11$

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