Question

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

Answer 1

Vertex form is just completeing th square

y=-2x^2+2x+2
first isolate the x terms
y=(-2x^2+2x)+2
undistribute the coefieicne infont of x^2 term
y=-2(x^2-x)+2
take 1/2 of -1 and square it (-1/2 sqared=1/4)
add negative and positive inside
y=-2(x^2-x+1/4-1/4)+2
complete the square
y=-2((x-1/2)^2)-1/4)+2
y=-2(x-1/2)^2+1/2+2
y=-2(x-1/2)^2+2.5

in form
y=a(x-h)^2+k
vertex=(h,k)
y=-2(x-1/2)^2+2.5
vertex is (0.5,2.5)

for x=6
input 6 for x and evaluate
y=-2(6)^2+2(6)+2
y=-2(36)+12+2
y=-72+14
y=-58



for x=6, the value is -58

the vertex form is
y=-2(x-1/2)^2+2.5
vetex is (0.5,2.5)