### Video Transcript

If π of π₯ is equal to π₯ squared
minus π₯ minus six and the solutions to the equation π₯ squared minus π₯ minus six
equals zero are three and negative two, then what are the points where π of π₯
intercepts the π₯-axis?

In this question, we have been
given a quadratic function π of π₯ equals π₯ squared minus π₯ minus six. We have also been told that the
equation π₯ squared minus π₯ minus six equals zero has two solutions, which are
three and negative two.

We can recall that the solution set
of a quadratic function can be found by setting π of π₯ equal to zero. In our case, we have that when π
of π₯ is equal to zero, π₯ squared minus π₯ minus six is also equal to zero. Hence, we can say that the
solutions to π of π₯ are three and negative two. Finding this is very useful in
helping us solve the question, since we know that the points where π of π₯ will
intercept the π₯-axis will be when π of π₯ is equal to zero.

Letβs take a minute to think as to
why this is the case. The equation we are sketching the
graph of is π¦ equals π of π₯. The π₯-axis is the same as the
equation π¦ equals zero. Hence, the points where π of π₯
intercepts the π₯-axis will be when these two lines intersect. So that is when π of π₯ is equal
to zero.

We have already found that when π
of π₯ equals zero, π₯ is equal to three or negative two. Hence, these are the π₯-coordinates
of the points where π of π₯ intercepts the π₯-axis. Since both of these points are on
the π₯-axis, we know that their π¦-coordinates must be zero.

Therefore, our solution to this
question is that the points where π of π₯ intercepts the π₯-axis are three, zero
and negative two, zero. Here is a quick sketch of what a
graph of π of π₯ may look like. We can see that it intersect the
π₯-axis at three, zero and negative two, zero.