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]
