tripiverded9

2021-12-30

$y=2\left(x-6\right)\left(x+1\right)$
a) What are the x intercepts?
b) What is the standart form of the equation?

### Answer & Explanation

peterpan7117i

Step 1
We have:
$y=2\left(x-6\right)\left(x+1\right)$
a) Put $y=0$
Or, $2\left(x-6\right)\left(x+1\right)=0$
Or, $\left(x-6\right)\left(x+1\right)=0$
Or, $x-6=0$ or $x+1=0$
Or, $x=6$ or $x=-1$
So, x-intercepts are: 6 and -1
b) We have:
$y=2\left(x-6\right)\left(x+1\right)$
Or, $y=2\left(x\left(x+1\right)-6\left(x+1\right)\right)$
Or, $y=2\left({x}^{2}+x-6x-6\right)$
Or, $y=2\left({x}^{2}-5x-6\right)$
Or, $y=2{x}^{2}-10x-12$

otoplilp1

Step 1
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation:
$y-\left(2×\left(x-6\right)×\left(x+1\right)\right)=0$
$y-2×\left(x-6\right)×\left(x+1\right)=0$
$y-2{x}^{2}+10x+12=0$
Solve $y-2{x}^{2}+10x+12=0$
In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.
We shall not handle this type of equations at this time.

karton

Step 1
Expand the expression
$y=2{x}^{2}-10x-12$
Step 2
Separate the constants and variables
$2{x}^{2}+10x=-y-12$
Step 3
Multiply or divide to change the leading coefficient to 1
${x}^{2}-5x=\frac{y+12}{2}$
Step 5
Separate the constants and variables
$\left(x-\frac{5}{2}{\right)}^{2}=\frac{y+12}{2}+\frac{25}{4}$
Step 6
Add or subtract the fractions
$\left(x-\frac{5}{2}{\right)}^{2}=\frac{2y+49}{4}$
Step 7
Take the root of both sides
$x-\frac{5}{2}=\sqrt{2y+49}4$ or $x-\frac{5}{2}=-\sqrt{\frac{2y+49}{4}}$
Solve
$x=\frac{\sqrt{2y+49}+5}{2}$ or $x=\frac{-\sqrt{2y+49}+5}{2}$
Step 8
b) Use the distributive property to multiply 2 by x-6
y=(2x-12)(x+1)
Use the distributive property to multiply 2x-12 by x+1 and combine like terms.
$y=2{x}^{2}-10x-12$

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