Let’s look at how to use formulas for a parabola to get certain important points on a parabola.

**Problem** For the parabola y = 2*x*^{2} + 3*x* – 2, locate the points below.

a. The *y*-intercept.

**Solution **At the y-intercept, the x value is zero. This means that we need to set *x* = 0 in the equation:

*y* = 2(0^{2}) + 3(0) – 2 = -2

Putting this together, the y-intercept is at (0, -2).

b. The vertex.

**Solution **The vertex is located using the formula where the values of *a*, *b*, and *c* come from the equation. In this case, *a* = 2, *b* = 3, and *c* = -2. This gives an *x* value on the intercept of

To find the corresponding y value, put this value into the equation,

This means the vertex is at (-^{3}/_{4}, –^{25}/_{8}).

c. The *x*-intercepts.

**Solution **At the x-intercepts, the *y* value is zero. Putting this into the equation yields

0 = 2*x*^{2} + 3*x* – 2

This equation is solved with the quadratic formula,

Put the values from the equation (*a* = 2, *b* = 3, and *c* = -2),

The x intercepts are at (-2, 0) and (^{1}/_{2}, 0).

All of these points are shown in the graph of the parabola below.