The graph of a quadratic function is a parabola. A parabola can cross the *x*-axis once, twice, or never. These points of intersection are called ** x-intercepts. **Does this concept sound familiar, yet strange? Your teacher may call these points by their nicknames.

### Other Terms for *x*-intercepts

- Zeros
- Roots
- Solutions
- Solution set

### Four Methods of Finding the *x*-intercepts

### A Parabola with Two X-intercepts

Use your finger to trace the green parabola. Notice that your finger touches the *x*-axis at (-3,0) and (4,0).

Therefore, the *x*-intercepts are (-3,0) and (4,0)

Be careful: the *x*-intercepts are not merely -3 and 4. The answer should be an ordered pair. Notice that the *y*-value of of these points is always 0.

### A Parabola with One x-intercept

Use your finger to trace the blue parabola. Notice that your finger touches the *x*-axis at (3,0).

Therefore, the *x*-intercept is (3,0).

Question: When a parabola has only one *x*-intercept, is the vertex always the *x*-intercept?

### A Parabola Without x-intercepts

Use your finger to trace the blue parabola. Does your finger touch the *x*-axis? No. Therefore, this parabola has no x-intercepts.