Question Video: Finding the Solution Set of a Quadratic Equation Graphically Mathematics • 9th Grade

The diagram shows the graph of 𝑦 = 𝑓(𝑥). What is the solution set of the equation 𝑓(𝑥) = 0?

01:28

Video Transcript

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

When we’re looking for 𝑓 of 𝑥 equal to zero, we’re interested in the place where 𝑦 equals zero. The origin of our graph is the place where 𝑦 equals zero and 𝑥 equals zero. 𝑦 equal zero represents a height that is not positive or negative, a height of zero. The line 𝑦 equals zero is the 𝑥-axis. And the place where our function crosses the 𝑥-axis is called the 𝑥-intercepts.

In this function, there’s an intercept at negative three, zero and at one, zero. A solution set of 𝑓 of 𝑥 equals zero is the set of 𝑥-values for which 𝑓 of 𝑥 is zero. We’re looking for the 𝑥-values that when you put them into the function, the 𝑦-value equals zero. And that’s going to be one and negative three. Set notation is the curly brackets. The two places that make this equation equal to zero is negative three and one for 𝑥.