For the given quadratic equation convert into vertex form, find the vertex, and find the value for x = 6. Show your work.

y = -2x2 + 2x +2
-(1/2)y=x^2-x-1
(-1/2)y+1=x^2-x
(-1/2)y+1=(x-1/2)^2-14
(-1/2)y=(x-1/2)^2-5/4
y=-2(x-1/2)^2+5/2

Is this right ?

2 x^2 - 2 x - 2 = -y

x^2 - x -1 = -(y/2)

x^2 - x = -y/2 + 1

x^2 - x + 1/4 = -y/2 + 1 + 1/4

(x- 1/2)^2 = -(1/2) (y - 5/2)

vertex at ( 1/2 , 5/2 )

if x = 6
y = - 2(36) + 12 + 2 = -58

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check
(5.5)^2 =? -1/2 (-60.5) ???
30.25 = 30.25 sure enough :)

Thank you :)

which one is the right answer and work

Yes, your conversion of the quadratic equation to vertex form and the subsequent steps to find the vertex and the value of x = 6 are correct.

To convert the given quadratic equation, y = -2x^2 + 2x + 2, to vertex form, you followed these steps:
1. Rewrite the equation by factoring out -2 from the x^2 and x terms: y = -2(x^2 - x - 1).
2. Complete the square for the expression inside the parentheses. You take the coefficient of the x term (in this case, -1), divide it by 2, and square it: (-1/2)^2 = 1/4.
3. Add this value inside the parentheses and subtract its equivalent value outside the parentheses to maintain the equality: -2(x^2 - x + 1/4 - 1/4 - 1).
4. Simplify the expression inside the parentheses: -2((x - 1/2)^2 - 5/4).
5. Distribute the -2 to both terms inside the parentheses: -2(x - 1/2)^2 + 5/2.
6. Now, the equation is in the vertex form: y = -2(x - 1/2)^2 + 5/2.

To find the vertex, you use the formula (h, k), where h is the x-coordinate and k is the y-coordinate. In this case, the vertex is (1/2, 5/2).

To find the value of y when x = 6, you substitute x = 6 into the vertex form equation:
y = -2(6 - 1/2)^2 + 5/2.

Now, you can evaluate this expression to find the value of y.