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

The graph shows the function π(π₯) = π₯Β² β 2π₯ + 3. What is the solution set of π(π₯) = 0?

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### Video Transcript

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

If weβre looking for π of π₯ equal to zero, weβ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 π¦ equals zero. And we know that π¦ equals zero along the π₯-axis. In order for this function to have a solution of π 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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