Question Video: Finding the Solution Set of a Quadratic Equation Graphically | Nagwa Question Video: Finding the Solution Set of a Quadratic Equation Graphically | Nagwa

Question Video: Finding the Solution Set of a Quadratic Equation Graphically Mathematics • Third Year of Preparatory School

The graph shows the function 𝑓(𝑥) = 𝑥² − 2𝑥 + 3. What is the solution set of 𝑓(𝑥) = 0?

01:07

Video Transcript

The graph shows the function 𝑓 of 𝑥 equals 𝑥 squared minus two 𝑥 plus three. What is the solution set of 𝑓 of 𝑥 equals zero.

Given some graph of a function 𝑦 equals 𝑓 of 𝑥, the solutions to the equation 𝑓 of 𝑥 equals zero correspond to the values of the 𝑥-intercepts if they exist. If there are no 𝑥-intercepts, it follows that there are no solutions to the equation 𝑓 of 𝑥 equals zero. Now in this case, we’ve been given the graph of the function 𝑓 of 𝑥 equals 𝑥 squared minus two 𝑥 plus three and asked to solve 𝑓 of 𝑥 equals zero or, in other words, 𝑥 squared minus two 𝑥 plus three equals zero.

But if we look carefully, we see that there are no locations where the graph, which is the green plot here, intersects the 𝑥-axis. And so, there are no real solutions to the equation 𝑓 of 𝑥 equals zero. In order to use set notation, we need to find a way to show that there are no values inside the set. So we use the notation shown. It’s the null set or empty set.

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