Question

Graph f(x)=2x^2-2x-1

Answer 1

It's a quadratic, so easiest is to complete the square to put in vertex form. Then:
\[y=2x ^{2}-2x-1\]
\[y=2(x ^{2}-x+?)-1-?\]
\[y=2(x ^{2}-x+\frac{ 1 }{4})-1-\frac{1}{2}\]
\[y=2(x-\frac{ 1 }{2}) ^{2}-\frac{3}{2}\]

So it's an upward opening parabola with vertex at (1/2, -3/2) and a vertical stretch by a factor of 2. Find the y-intercept by setting x=0 at (0,-1). Also find the x-intercepts with the quadratic formula.