Question

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

Answer 1

Part 1) The vertex is the point (0.50,2.50)

part 2)
`y=-58`

Explanation:

we have

`y=-2x^(2) +2x+2`

Part 1) Convert into vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`y-2=-2x^(2) +2x`

Factor the leading coefficient

`y-2=-2(x^(2) -x)`

Complete the square. Remember to balance the equation by adding the same constants to each side

`y-2-0.50=-2(x^(2) -x+0.25)`

`y-2.50=-2(x^(2) -x+0.25)`

`y-2.50=-2(x-0.50)^(2)`

`y=-2(x-0.50)^(2)+2.50` -----> equation in vertex form

The vertex is the point (0.50,2.50)

Part 2) Find the value of y for x=6

substitute the value of x in the equation

`y=-2(6)^(2) +2(6)+2`

`y=-72 +12+2`

`y=-58`