What is the factored form of $y = - 2 x^{2} + 2 x + 2$ $y= -2x^2+2x+2$ ?

Question

What is the factored form of $y = - 2 x^{2} + 2 x + 2$ $y= -2x^2+2x+2$ ?

1 Answer

Impact of this question

1650 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-11T07:18:33

$y = - 2 (x - \frac{1}{2} - \frac{\sqrt{5}}{2}) (x - \frac{1}{2} + \frac{\sqrt{5}}{2})$ $y = -2(x-1/2 - sqrt(5)/2)(x-1/2 + sqrt(5)/2)$

Explanation:

Separate out the scalar factor $- 2$ $-2$ , complete the square, then use the difference of squares identity.

The difference of squares identity can be written:

$a^{2} - b^{2} = (a - b) (a + b)$ $a^2-b^2 = (a-b)(a+b)$

We use this with $a = (x - \frac{1}{2})$ $a=(x-1/2)$ and $b = \frac{\sqrt{5}}{2}$ $b=sqrt(5)/2$ as follows:

$y = - 2 x^{2} + 2 x + 2$ $y = -2x^2+2x+2$

$y = - 2 (x^{2} - x - 1)$ $color(white)(y) = -2(x^2-x-1)$

$y = - 2 (x^{2} - x + \frac{1}{4} - \frac{5}{4})$ $color(white)(y) = -2(x^2-x+1/4 - 5/4)$

$y = - 2 ⎛ ⎝ {(x - \frac{1}{2})}^{2} - {(\frac{\sqrt{5}}{2})}^{2} ⎞ ⎠$ $color(white)(y) = -2((x-1/2)^2 - (sqrt(5)/2)^2)$

$y = - 2 ((x - \frac{1}{2}) - \frac{\sqrt{5}}{2}) ((x - \frac{1}{2}) + \frac{\sqrt{5}}{2})$ $color(white)(y) = -2((x-1/2) - sqrt(5)/2)((x-1/2) + sqrt(5)/2)$

$y = - 2 (x - \frac{1}{2} - \frac{\sqrt{5}}{2}) (x - \frac{1}{2} + \frac{\sqrt{5}}{2})$ $color(white)(y) = -2(x-1/2 - sqrt(5)/2)(x-1/2 + sqrt(5)/2)$

Science

Math

Humanities

... and beyond

What is the factored form of $y = - 2 x^{2} + 2 x + 2$ $y= -2x^2+2x+2$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

What is the factored form of y=−2x2+2x+2y= -2x^2+2x+2?

1 Answer

Explanation:

Related questions

Impact of this question

What is the factored form of $y = - 2 x^{2} + 2 x + 2$ $y= -2x^2+2x+2$ ?