Answer:
Part 1) The vertex is the point (0.50,2.50)
part 2) [tex]y=-58[/tex]
Step-by-step explanation:
we have
[tex]y=-2x^{2} +2x+2[/tex]
Part 1) Convert into vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]y-2=-2x^{2} +2x[/tex]
Factor the leading coefficient
[tex]y-2=-2(x^{2} -x)[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]y-2-0.50=-2(x^{2} -x+0.25)[/tex]
[tex]y-2.50=-2(x^{2} -x+0.25)[/tex]
[tex]y-2.50=-2(x-0.50)^{2}[/tex]
[tex]y=-2(x-0.50)^{2}+2.50[/tex] -----> 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
[tex]y=-2(6)^{2} +2(6)+2[/tex]
[tex]y=-72 +12+2[/tex]
[tex]y=-58[/tex]
