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

Video Transcript

The diagram shows the graph of 𝑦 equals 𝑓 of 𝑥. What is the solution set of the equation 𝑓 of 𝑥 equals zero?

Remember, given the graph of a quadratic equation 𝑓 of 𝑥 equals 𝑎𝑥 squared plus 𝑏𝑥 plus 𝑐, the solutions to the quadratic equation 𝑓 of 𝑥 equals zero correspond to the values of the 𝑥-intercepts. So all we need to do is identify the location of the 𝑥-intercepts on our graph. Locating these, we see that there is, in fact, only one 𝑥-intercept. It’s negative two. So there’s actually only one solution to the equation 𝑓 of 𝑥 equals zero. That’s 𝑥 equals negative two. Now we have in fact been asked to give the solution set to the equation 𝑓 of 𝑥 equals zero. So in set notation, it’s the set containing the single element negative two.