#f(x) = -2x^2+2x+8 or f(x) = -2(x^2-x)+8 # or
#f(x) = -2{x^2-x +(1/2)^2}+1/2+8 # or
#f(x) = -2(x-1/2)^2+1/2+8 # or
#f(x) = -2(x-0.5)^2+8.5# . Comparing with vertex form of
equation #f(x) = a(x-h)^2+k ; (h,k)# being vertex we find
here #h=0.5 , k=8.5 :.# Vertex is at #(0.5,8.5) # . y intercept
is found by putting #x=0# in the equation #y = -2x^2+2x+8# or
#y=8 :.# y intercept is #y=8 or (0,8)#
x intercept is found by putting #y=0# in the equation
#y = -2x^2+2x+8 or -2x^2+2x+8=0 # or
#-2(x-0.5)^2+8.5 =0 or 2(x-0.5)^2 = 8.5 # or
#(x-0.5)^2 = 4.25 or (x-0.5) = +- sqrt4.25# or
#x = 0.5 +- sqrt4.25 or x ~~ 2.56 (2 dp) , x ~~ -1.56 (2 dp)#
x intercepts are at #(-1.56,0) and (2.56,0)#
graph{-2x^2+2x+8 [-20, 20, -10, 10]} [Ans]
