# Chapter 4 Quadratic Functions and Factoring - 4.7 Complete the Square - 4.7 Exercises - Skill Practice - Page 289: 44

The vertex form of the function is $y=(x-(-10))^{2}+(10).$ The vertex is $(-10,-10)$.

#### Work Step by Step

$y=x^{2}+20x+90\qquad$ ...write in form of $x^{2}+bx=c$ (add $-90$ to each side). $y-90=x^{2}+20x\qquad$ ...square half the coefficient of $x$. $(\displaystyle \frac{20}{2})^{2}=(10)^{2}=100\qquad$ ...complete the square by adding $100$ to each side of the expression $y-90+100=x^{2}+20x+100\qquad$ ... write $x^{2}+20x+100$ as a binomial squared. $y+10=(x+10)^{2}\qquad$ ...add $-10$ to each side of the expression $y=(x+10)^{2}-10\qquad$ ...write in vertex form $y=a(x-h)^{2}+k$. $y=(x-(-10))^{2}+(10)$ The vertex form of a quadratic function is $y=a(x-h)^{2}+k$ where $(h,k)$ is the vertex of the function's graph. Here, $h=-10,\ k=-10$, so the vertex is $(-10,-10)$

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