To find where a quadratic function touches the axes, you can do it in two ways: by looking at a graph or by using math calculations.

Finding Intercepts by Looking at the Graph:

1. Y-Intercept: This is where the graph meets the y-axis. You can find it at the point (0, f(0)). This means you look at the function's value when x is 0.

2. X-Intercepts: These are the points where the graph hits the x-axis. You find them by figuring out where f(x) equals 0.

Finding Intercepts Using Math:

1. Y-Intercept: To find this, just plug in 0 for x in the function.

2. X-Intercepts: You can find these by solving the equation (ax^2 + bx + c = 0). You can use methods like factoring, completing the square, or using the quadratic formula: [ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

For example, if you have the function (f(x) = x^2 - 4x + 3):

• The y-intercept is (0, 3).
• The x-intercepts are (1, 0) and (3, 0).

These points tell you where the graph crosses the axes!