Question

Convert f(x)=2x^2+2x+7 into vertex form.

Answer 1

Complete the square to get vertex form

Answer 2

A step-by-step would be fantastic

Answer 3

Or a more detailed explanation...

Answer 4

Alright, first factor out the number in front of x^2

2(x^2+x+7/2)

Now take the coefficient of the x with no exponent, divide it by 2, and then square it. What do you get?

Answer 5

.25?

Answer 6

why are you dividing by 2 within that "2(x^2+x+7/2)?

Answer 7

Yep, or 1/4. Now were gonna both add and subtract that after the x.

2(x^2+x+1/4-1/4+7/2)

Answer 8

The coefficient in front of the x with no exponent, which is 1

Answer 9

Its just what you do,

Answer 10

\[\frac{2(x ^{2}+x+\frac{ 1 }{ 4 }-\frac{ 1 }{ 4 }+7}{2}\]

Answer 11

with that () closed off. is that what it should look like?

Answer 12

Oh no, the 2 is only under the 7

Answer 13

Because first we factored out the 2

Answer 14

so when we factor out a 2, we also divide 7 by 2?

Answer 15

Yep we divided everything by 2 which is why the 2x^2+2x part became x^2+x

Answer 16

I think i understand...

Answer 17

so id be \[f(x) = 2 ( x ^{2} + x ) + \frac{ 7 }{ 2 }\]

Answer 18

?

Answer 19

Nope, how does the x^2+x+1/4 factor?

Answer 20

In 2(x^2+x+1/4-1/4+7/2)

Answer 21

(x+1/2)^2 right?

Answer 22

So now we have 2((x+1/2)^2-1/4+7/2)

Answer 23

-1/4+7/2=?