write in the equation standard form f(x)=-2x^2-x + 4, find f(-2)

Question

please explain how to write the equation of this line in standard form

Answer 1

f(x)=4-2x^2-x; f(x)=4-2(x^2+x/2)=4-2(x^2+x/2+(1/4)^2)-(1/4)^2=4-2(x+1/2)^2-(1/4)^2=

4-1/16-2(x+1/2)^2; f(x)=63/16-2(x+1/2)^2 in standard form. When x=-1/2, f(x)=63/16 ("y" intercept), origin and vertex; when f(x)=0, (x+1/2)^2=63/32 so x=-1/2+sqrt(63/32)=-1/2+(3/8)sqrt(14) are the x intercepts (parabola, inverted U shape).

f(-2)=4-2*4-(-2)=6-8=-2.