Question Video: Understanding Zeros of Quadratic Functions Mathematics

If the graph of the quadratic function 𝑓 cuts the π‘₯-axis at the points (βˆ’3, 0) and (βˆ’9, 0), what is the solution set of 𝑓(π‘₯) = 0 in ℝ?

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Video Transcript

If the graph of the quadratic function 𝑓 cuts the π‘₯-axis at the points negative three, zero and negative nine, zero, what is the solution set of 𝑓 of π‘₯ equals zero in the set of real numbers?

Now remember, if we’re given the graph of a function, we can find the solutions to 𝑓 of π‘₯ equals zero by locating the π‘₯-intercepts or zeros of the function. Now, in this case, we’re not actually given a graph, but we are told the coordinates at which the function cuts the π‘₯-axis. It’s negative three, zero and negative nine, zero. Since the first number in each ordered pair corresponds to the value of π‘₯ here, we can say that the solutions to the equation 𝑓 of π‘₯ equals zero are π‘₯ equals negative three and π‘₯ equals negative nine. Using set notation, the solution set of 𝑓 of π‘₯ equals zero in the set of real numbers is the set containing the elements negative three and negative nine.

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