Question

Can someone help me please?

For the given quadratic equation convert into vertex form, find the vertex, and find the value for x = 6.
y = -2x2 + 2x +2

Answer 1

Do you know how to complete the square?

Answer 2

no I do not

Answer 3

You should look it up. Give an effort to learn it. I'll help if you try and it doesn't work.

Answer 4

btw that is -2x^2

Answer 5

I know

Answer 6

every example so far they haven't had to substitute 6 for x. Not only that but they don't have a negative x^2 and they = 0 not y.

Answer 7

I really like the effort that you have put forth.

Answer 8

\[
y = -2x^2 + 2x +2
\]If you divide by \(-2\), then: \[
-\frac{y}{2} = x^2-x-1
\]

Answer 9

Do you think you can complete the square on the right side now?

Answer 10

Don't worry about substitute for \(6\) just yet.

Answer 11

I am really lost on what the next step would be. From what I see you would try to remove the square but I don't know how to do that.

Answer 12

Now, you create the square.

Answer 13

A square would be the following:\[
(x+a)^2
\]

Answer 14

Where \(a\) is some number.

Answer 15

When you foil, you get: \[
(x+a)^2=x^2+2ax+a^2
\]

Answer 16

We have to match it up with what we have.

Answer 17

Since we have \(x^2 + (-1)x+(-1)\)

Answer 18

The \(2a =-1\) when we match it up.

Answer 19

This means \(a=-1/2\)

Answer 20

And \(a^2=1/4\).

Answer 21

So \[
(x-1/2)^2 = x^2-x+1/4
\]

Answer 22

This would mean that: \[
x^2-x -1 + 1/4 - 1/4 = (x-1/2)^2-1-1/4 = (x-1/2)^2-5/4
\]

Answer 23

\[
-y/2= (x-1/2)^2-5/4
\]We can multiply by negative \(-2\) again and: \[
y=-2(x-1/2)^2+5/2
\]

Answer 24

This is the vertex form.

Answer 25

I am so confused

Answer 26

Okay, I will do it one more time.

Answer 27

I really don't understand how you went from (x+a)^2 to all of that.

Answer 28

We have \(x^2-x\), we only want to focus on this part.

Answer 29

We take the coefficient of \(x\), in this case it is \(-1\), because \(x^2-x = x^2+(-1)x\)

Answer 30

Do you follow?

Answer 31

No