The slope is m and the y-intercept is b. We wish to do the same with the graphs of quadratic functions. We will use several ideas that were touched on in past hours to provide a scheme for knowing how to graph a quadratic function. The first thing to notice about a parabola is its symmetry . If you flip this parabola about the y-axis, you get the exact same parabola.
Every parabola has such a line of symmetry.
The point at which the parabola meets its line of symmetry is called the vertex of the parabola. We take one possibility at a time. Suppose that the coefficients b and c are both 0. To find out, let a be a few different values and compare the values of a with the corresponding shapes of the sketches that we get. The sketches below suggest the role of a .