Question Video: Given a Graph of a Quadratic Function Identify the 𝑥-Intercepts | Nagwa Question Video: Given a Graph of a Quadratic Function Identify the 𝑥-Intercepts | Nagwa

# Question Video: Given a Graph of a Quadratic Function Identify the π₯-Intercepts Mathematics • Third Year of Preparatory School

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Identify the π₯-intercepts of the quadratic function π(π₯) = π₯Β² β 1.

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### Video Transcript

Identify the π₯-intercepts of the quadratic function π of π₯ equals π₯ squared minus one.

We have the function π of π₯ equals π₯ squared minus one and a graph of that function. Recall that the π₯-intercepts of a function are the places where the graph of that function crosses the π₯-axis. Theyβre located at some point π₯, zero. On our graph, we see them here and here. The scale of the π₯-axis on this graph is marked in twos. On the right side, halfway between zero and two is the place where the graph crosses the π₯-axis. We see that the scale is further divided into four smaller squares, which helps us identify exactly where this graph crosses the π₯-axis. In this case, itβs one and negative one.

Here, we only had to look at the graph to find out where the π₯-intercepts are. However, sometimes itβs hard to get accurate information from a graph. So itβs helpful to know how to find these values algebraically using the function. If we know that π of π₯ equals π₯ squared minus one, the π₯-intercepts will be located where π of π₯ equals zero. By setting π of π₯ equal to zero and then solving for π₯, we can find the π₯-intercepts. If we add one to both sides, then one equals π₯ squared. From there, we take the square root of both sides. The square root of one is plus or minus one, and the square root of π₯ squared equals π₯. This confirms the intercepts we found from the graph. We have an intercept at negative one and an intercept at one.

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