Video: Finding the Solution Set of a Quadratic Equation Graphically

The diagram shows the graph of 𝑦 = 𝑓(π‘₯). What is the solution set of the equation 𝑓(π‘₯) = 0?

01:01

Video Transcript

The diagram shows the graph of 𝑦 equals 𝑓 of π‘₯. What is the solution set of the equation 𝑓 of π‘₯ equals zero?

We know that 𝑦 equals 𝑓 of π‘₯. And we’re looking for the place where 𝑓 of π‘₯ equals zero. That will be the place for this quadratic where 𝑦 equals zero. And 𝑦 equals zero at the π‘₯-intercept. 𝑦 equals zero along the π‘₯-axis. And this function is crossing the π‘₯-axis at negative two. Therefore, the π‘₯-intercept is negative two, zero. But the solution set will be the π‘₯-value that makes 𝑓 of π‘₯ equal to zero. And that means instead of coordinate form, we’re only interested in the π‘₯-coordinate. This function equals zero when π‘₯ equals negative two. Therefore, the solution set will only include the value negative two.

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