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

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