Video: Graphical Solutions to Quadratic Equations

The curve of a quadratic function, 𝑓, intersects the π‘₯-axis at the points (1, 0) and (βˆ’4, 0). What is the solution set of the equation 𝑓(π‘₯) = 0?

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Video Transcript

The curve of a quadratic function 𝑓 intersects the π‘₯-axis at the points one, zero and negative four, zero. What is the solution set of the equation 𝑓 of π‘₯ equals zero?

Let’s sketch out what we know. We know that 𝑓 intersects the π‘₯-axis at these two points: one, zero and negative four, zero. We also know that we’re dealing with a quadratic function. Maybe the quadratic function looks like this. Maybe it looks like this. But we don’t actually need that information to find the solution set.

The place where 𝑓 of π‘₯ equals zero is the π‘₯ value of the π‘₯-intercepts. This happens at π‘₯ equals negative four and π‘₯ equal to positive one. Our solution set is the set of these two π‘₯ values: negative four and one.

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