Video: Graphical Solutions to Quadratic Equations

Video Transcript

The curve of a quadratic function 𝑓 intersects the 𝑥-axis at the points one, zero and negative four, zero. What is the solution set of the equation 𝑓 of 𝑥 equals zero?

Let’s sketch out what we know. We know that 𝑓 intersects the 𝑥-axis at these two points: one, zero and negative four, zero. We also know that we’re dealing with a quadratic function. Maybe the quadratic function looks like this. Maybe it looks like this. But we don’t actually need that information to find the solution set.

The place where 𝑓 of 𝑥 equals zero is the 𝑥 value of the 𝑥-intercepts. This happens at 𝑥 equals negative four and 𝑥 equal to positive one. Our solution set is the set of these two 𝑥 values: negative four and one.