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

Join Nagwa Classes

Attend live Mathematics sessions on Nagwa Classes to learn more about this topic from an expert teacher!

Identify the π‘₯-intercepts of the quadratic function 𝑓(π‘₯) = π‘₯Β² βˆ’ 1.

01:41

Video Transcript

Identify the π‘₯-intercepts of the quadratic function 𝑓 of π‘₯ equals π‘₯ squared minus one.

We have the function 𝑓 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. They’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, it’s one and negative one.

Here, we only had to look at the graph to find out where the π‘₯-intercepts are. However, sometimes it’s hard to get accurate information from a graph. So it’s helpful to know how to find these values algebraically using the function. If we know that 𝑓 of π‘₯ equals π‘₯ squared minus one, the π‘₯-intercepts will be located where 𝑓 of π‘₯ equals zero. By setting 𝑓 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.

Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

  • Interactive Sessions
  • Chat & Messaging
  • Realistic Exam Questions

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy