Video: Finding the Solution Set of a Quadratic Function from Its Graph When 𝑓(π‘₯) = 0

The graph shows the function 𝑓(π‘₯) = π‘₯Β² βˆ’ 2π‘₯ + 3. What is the solution set of 𝑓(π‘₯) = 0?

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Video Transcript

The graph shows the function 𝑓 of π‘₯ equals π‘₯ squared minus two π‘₯ plus three. What is the solution set of 𝑓 of π‘₯ equals zero?

If we’re looking for 𝑓 of π‘₯ equal to zero, we’re looking for the π‘₯-values that make π‘₯ squared minus two π‘₯ plus three equal to zero. And on the graph, that will be the place where 𝑦 equals zero. And we know that 𝑦 equals zero along the π‘₯-axis. In order for this function to have a solution of 𝑓 of π‘₯ equals zero, it would need to cross the π‘₯-axis. This function does not cross the π‘₯-axis. Therefore, it has zero solutions or zero roots. And therefore, the solution set here is the empty set; there is no solution.

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