Question

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

Answer 1

`f(x)=-2x^(2)+2x+2 \\ \\ f(6)=-2*6^(2)+2*6+2=-2*36+12+2=-72+14=-58 \\ \\ f(x)=a(x-p)^(2)+q \\ \\ \Delta=2^(2)-4*(-2)*2=4+16=20 \\ \\ p= (-b)/(2a) \\ \\ p= (-2)/(-4) = (1)/(2) \\ \\ q= (-\Delta)/(4a) \\ \\ q= (-20)/(-8) = (5)/(2) \\ \\ f(x)=-2(x- (1)/(2))^(2)+ (5)/(2)`