# Question Video: Finding ๐ฅ-Intercepts from a Given Graph Mathematics

What are the ๐ฅ-intercepts of the function represented by the given graph?

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### Video Transcript

What are the ๐ฅ-intercepts of the function represented by the given graph?

In this question, weโre given the graph of a function, and weโre asked to determine the ๐ฅ-intercepts of the graph of this function. And we could first recall what we mean by the ๐ฅ-intercept of a function. Itโs the points on the graph of the function where the ๐ฆ-coordinate is equal to zero. And the ๐ฆ-coordinates of these points are represented by the vertical axis. And this means the horizontal line ๐ฆ is equal to zero contains all points with ๐ฆ-coordinate equal to zero.

Therefore, the ๐ฅ-intercepts of the function will be the points of intersection between the line ๐ฆ is equal to zero and the graph of the function. This is why theyโre called ๐ฅ-intercepts. The line ๐ฆ is equal to zero is the ๐ฅ-axis. And we can see this curve intersects the ๐ฅ-axis at two points: when ๐ฅ is negative one and when ๐ฅ is three. And remember, the ๐ฆ-coordinates of these points will be zero since they lie on the ๐ฅ-axis. Therefore, weโve shown the ๐ฅ-intercepts of the function represented by the graph are the points negative one, zero and three, zero.

And while this is enough to answer our question, itโs worth reiterating what is meant by the ๐ฅ-intercepts of a function. Why do we find these values? And what do they mean? Letโs start by giving our function a name. Letโs say itโs the function ๐ of ๐ฅ. In the graph of a function, the ๐ฅ-value of a point on the curve represents the input value of our function and the ๐ฆ-coordinate tells us the corresponding output of the function. For example, the vertex of this function is the point with coordinates one, four. When we input a value of one into our function, it outputs four. ๐ evaluated at one is four.

We can apply this exact same reasoning to the two ๐ฅ-intercepts of our function. This tells us ๐ evaluated at negative one is equal to zero, and ๐ evaluated at three is equal to zero. These are roots of the function. And the roots of functions tell us a lot of information about these functions, so theyโre useful to find. Therefore, we were able to show the ๐ฅ-intercepts of the function represented by the given graph are the points negative one, zero and three, zero.