Graphing a parabola

I have this equation: y = 2x^2 - 5x -3

I tried to find coordinates using the graph, then used a graphing calculator. (It's been a while since I used it, so I forgot how find the x-intercepts.  Mine is an older version also, TI-89.)

When I used the quadratic formula, however, I got completely differnt answers.

$$x \approx -.56

x \approx 2.97$$(Using Graphing calculator)

$$x=6

x=4$$(Using quadratic formula)

What kind of mistakes may I have made along the way?

Thanks for the help!