Video: Finding the Solution Set of a Quadratic Equation Graphically

The diagram shows the graph of π¦ = π(π₯). What is the solution set of the equation π(π₯) = 0?

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Video Transcript

The diagram shows the graph of π¦ equals π of π₯. What is the solution set of the equation π of π₯ equals zero?

π of π₯ equals zero. For π¦ equals π of π₯ means the places where π¦ equals zero. The origin of our graph is the place where π¦ equals zero and π₯ equals zero. π¦ equals zero would represent a height that is not positive or negative. π¦ equals zero at the π₯-intercepts. Itβs the place where our line crosses the π₯-axis. On this graph, we see, it crosses the π₯-axis twice, once when π₯ equals negative two, and once when π₯ equals positive two.

Written in set notation, we can say that negative two and two are the solutions. Be careful, set notation is not a coordinate point. Weβre not saying anything about the point negative two, two. Weβre saying if you plug in negative two or positive two in your equation, the output will be zero. These are the solutions.