# Video: Understanding Zeros of Quadratic Functions

If the graph of the quadratic function π cuts the π₯-axis at the points (β3, 0) and (β9, 0), what is the solution set of π(π₯) = 0 in β?

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### Video Transcript

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

Letβs use the information to sketch a graph: π₯-axis, π¦-axis, point negative three, zero, and point negative nine, zero. The graph could look like this. It could also look like this. Weβ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 π 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 π¦. We want a list of the π₯-coordinates for all the π₯-intercepts. And weβre giving our two intercepts. The solution set for π of π₯ equals zero is the π₯-coordinate negative three and negative nine. The set of negative three, negative nine.