Return to Assignments Quadratic functions and graphs

### Assignment 3

Given the function:

Answer the following questions:

- What is the intersection point of the graph with the -axis?
- Does the graph have intersection points with the -axis, and if so, how many? Calculate the coordinates.
- What is the symmetry axis?

### Solution

1. Because in the formula equals , the intersection point with the -axis equals .

2. In order to find out whether the graph of the function has intersection points with the -axis, we have to calculate the discriminant. However, we can also notice that the equation can be factorized:

Then we kill two birds with one stone. There are two intersection points with the -axis and their coordinates are and .

3. The symmetry axis lies just in the middle of these two points and thus the symmetry axis is .