# Question Video: Finding the Solution Set of a Quadratic Equation Graphically Mathematics • 9th Grade

The diagram shows the graph of ๐ฆ = ๐(๐ฅ). What is the solution set of the equation ๐(๐ฅ) = 0?

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### Video Transcript

The diagram shows the graph ๐ฆ equals ๐ of ๐ฅ. What is the solution set of the equation ๐ of ๐ฅ equals zero?

When weโre looking for ๐ of ๐ฅ equal to zero, weโre interested in the place where ๐ฆ equals zero. The origin of our graph is the place where ๐ฆ equals zero and ๐ฅ equals zero. ๐ฆ equal zero represents a height that is not positive or negative, a height of zero. The line ๐ฆ equals zero is the ๐ฅ-axis. And the place where our function crosses the ๐ฅ-axis is called the ๐ฅ-intercepts.

In this function, thereโs an intercept at negative three, zero and at one, zero. A solution set of ๐ of ๐ฅ equals zero is the set of ๐ฅ-values for which ๐ of ๐ฅ is zero. Weโre looking for the ๐ฅ-values that when you put them into the function, the ๐ฆ-value equals zero. And thatโs going to be one and negative three. Set notation is the curly brackets. The two places that make this equation equal to zero is negative three and one for ๐ฅ.