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

Accepted Solution

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 formGroup 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 formThe vertex is the point (0.50,2.50)Part 2) Find the value of y for x=6substitute 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]