Video: Understanding Zeros of Quadratic Functions

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 points negative three, zero and negative nine, zero, what is the solution set of 𝑓 of π‘₯ equals zero in all real numbers?

Let’s use the information to sketch a graph: π‘₯-axis, 𝑦-axis, point negative three, zero, and point negative nine, zero. The graph could look like this. It could also look like this. We’re not really given any other information about the graph except that it intersects the π‘₯-axis at negative three and negative nine. The solution set for 𝑓 of π‘₯ equal to zero in all real numbers.

Another way to phrase this is that we want the set of all the π‘₯-values that yield a zero-value for 𝑦. We want a list of the π‘₯-coordinates for all the π‘₯-intercepts. And we’re giving our two intercepts. The solution set for 𝑓 of π‘₯ equals zero is the π‘₯-coordinate negative three and negative nine. The set of negative three, negative nine.

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