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

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

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Answer 1 · 2017-04-12T12:37:52

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

Explanation:

Let us first simplify this.

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

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

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

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

$= 80 (x^{2} + 2 \times \frac{21}{80} x + {(\frac{21}{80})}^{2} - {(\frac{21}{80})}^{2}) + 34$ $=80(x^2+2xx21/80x+(21/80)^2-(21/80)^2)+34$

$= 80 {(x^{2} + \frac{21}{80})}^{2} - {(\frac{21}{80})}^{2} \times 80 + 34$ $=80(x^2+21/80)^2-(21/80)^2xx80+34$

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

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

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

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

Answer 2 · 2017-04-12T12:38:22

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

Explanation:

Let us first simplify this.

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

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

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

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

$= 80 (x^{2} + 2 \times \frac{21}{80} x + {(\frac{21}{80})}^{2} - {(\frac{21}{80})}^{2}) + 34$ $=80(x^2+2xx21/80x+(21/80)^2-(21/80)^2)+34$

$= 80 {(x^{2} + \frac{21}{80})}^{2} - {(\frac{21}{80})}^{2} \times 80 + 34$ $=80(x^2+21/80)^2-(21/80)^2xx80+34$

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

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

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

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

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

2 Answers

Explanation:

Explanation:

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Science

Math

Humanities

... and beyond

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

2 Answers

Explanation:

Explanation:

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