2022-01-28

What is the standard form of $y=-5{\left(x-8\right)}^{2}+11$?

Souticexi

Expert

Explanation:
The Standard Form for writing a polynomial is to put the terms with the highest degree first (what index it is raised to).
First, lets

Micheal Hensley

Expert

Explanation:
The standard form of the quadratic equation is
$y=a{x}^{2}+bx+c$
However, you have been given an equation in vertex form
$y=-5{\left(x-8\right)}^{2}+11$
First, factor out the ${\left(x-8\right)}^{2}$ term using the FOIL process
y=-5(x-8)(x-8)+11
$y=-5\left({x}^{2}-8x-8x+64\right)+11$
$y=-5\left({x}^{2}-16x+64\right)+11$
Next, multiply the -5 through the factored expression.
$y=-5{x}^{2}+80x-320+11$
Finally, add the last two terms
$y=-5{x}^{2}+80x-309$

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