# What is the vertex form of y= (5x+2)^2 + 11x(5x+2)+30?

Apr 12, 2017

$y = 80 {\left({x}^{2} + \frac{21}{80}\right)}^{2} + \frac{2279}{80}$

#### Explanation:

Let us first simplify this.

$y = {\left(5 x + 2\right)}^{2} + 11 x \left(5 x + 2\right) + 30$

$= 25 {x}^{2} + 20 x + 4 + 55 {x}^{2} + 22 x + 30$

$= 80 {x}^{2} + 42 x + 34$

$= 80 \left({x}^{2} + \frac{42}{80} x\right) + 34$

$= 80 \left({x}^{2} + 2 \times \frac{21}{80} x + {\left(\frac{21}{80}\right)}^{2} - {\left(\frac{21}{80}\right)}^{2}\right) + 34$

$= 80 {\left({x}^{2} + \frac{21}{80}\right)}^{2} - {\left(\frac{21}{80}\right)}^{2} \times 80 + 34$

$= 80 {\left({x}^{2} + \frac{21}{80}\right)}^{2} - \frac{441}{80} + 34$

$= 80 {\left({x}^{2} + \frac{21}{80}\right)}^{2} + \frac{2279}{80}$

which is in vertex form and vertex is $\left(- \frac{21}{80} , \frac{2279}{80}\right)$ or $\left(- \frac{21}{80} , 28 \frac{39}{80}\right)$ and graph appears as follows:

graph{80x^2+42x+34 [-2, 2, -10.9, 149.1]}

Apr 12, 2017

$y = 80 {\left({x}^{2} + \frac{21}{80}\right)}^{2} + \frac{2279}{80}$

#### Explanation:

Let us first simplify this.

$y = {\left(5 x + 2\right)}^{2} + 11 x \left(5 x + 2\right) + 30$

$= 25 {x}^{2} + 20 x + 4 + 55 {x}^{2} + 22 x + 30$

$= 80 {x}^{2} + 42 x + 34$

$= 80 \left({x}^{2} + \frac{42}{80} x\right) + 34$

$= 80 \left({x}^{2} + 2 \times \frac{21}{80} x + {\left(\frac{21}{80}\right)}^{2} - {\left(\frac{21}{80}\right)}^{2}\right) + 34$

$= 80 {\left({x}^{2} + \frac{21}{80}\right)}^{2} - {\left(\frac{21}{80}\right)}^{2} \times 80 + 34$

$= 80 {\left({x}^{2} + \frac{21}{80}\right)}^{2} - \frac{441}{80} + 34$

$= 80 {\left({x}^{2} + \frac{21}{80}\right)}^{2} + \frac{2279}{80}$

which is in vertex form and vertex is $\left(- \frac{21}{80} , \frac{2279}{80}\right)$ or $\left(- \frac{21}{80} , 28 \frac{39}{80}\right)$ and graph appears as follows:

graph{80x^2+42x+34 [-2, 2, -10.9, 149.1]}