x- and y-intercepts

Glossary Checklist FAQ

x- and y-intercepts

In the Investigation, you investigated the values of \(a\) and \(q\) and the resulting number of \(x\)-intercepts. What conclusions can be made?

What about the \(y\)-intercept(s), can there be more than one? The definition of a function is that there is only one output for every input. A \(y\)-intercept has an input of \(x = 0\). Because the \(y\)-intercept is an output for \(x = 0\), there can only be one \(y\)-intercept for any quadratic function. Can there be zero \(y\)-intercepts? No, there must be one, and only one \(y\)-intercept.

To understand this, it is best to look at some examples.