You can rewrite the equation as
y/2 = x^2 + b/2*x + 2
y/2 = x^2 + 2*b/4*x + (b/4)^2 - (b/4)^2 + 2
(x + b/2)^2 = 1/2*[y + (b^2/8 - 4)]
It is the equation of the parabola. Now see how it changes with b.
draw the graph of y=2x^2 + bx + 4 for different values of b. How does changing b affect the curve ax^2 +bx + c?
i drew several graphs and i cant really 'see' anything. ive compared coordinates of turning points etc. but i dont get it. any help?