Question Video: Identifying the x-axis Intersections of a Quadratic Function | Nagwa Question Video: Identifying the x-axis Intersections of a Quadratic Function | Nagwa

# Question Video: Identifying the x-axis Intersections of a Quadratic Function Mathematics • Third Year of Preparatory School

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If π(π₯) = π₯Β² β π₯ β 6, and the solutions to the equation π₯Β² β π₯ β 6 = 0 are {3, β2}, then what are the points where π(π₯) intercepts the π₯-axis?

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### 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.

Letβs 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.

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