Video: Finding the Solution Set of a Quadratic Equation Graphically

The diagram shows the graph of 𝑦 = 𝑓(π‘₯). What is the solution set of the equation 𝑓(π‘₯) = 0?

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Video Transcript

The diagram shows the graph of 𝑦 equals 𝑓 of π‘₯. What is the solution set of the equation 𝑓 of π‘₯ equals zero?

𝑓 of π‘₯ equals zero. For 𝑦 equals 𝑓 of π‘₯ means the places where 𝑦 equals zero. The origin of our graph is the place where 𝑦 equals zero and π‘₯ equals zero. 𝑦 equals zero would represent a height that is not positive or negative. 𝑦 equals zero at the π‘₯-intercepts. It’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. We’re not saying anything about the point negative two, two. We’re saying if you plug in negative two or positive two in your equation, the output will be zero. These are the solutions.

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