Question Video: Determining Where the Graph of a Quadratic Equation in Factored Form Crosses the 𝑥-Axis Mathematics

At which values of 𝑥 does the graph of the equation 𝑦 = (𝑥 + 2)(𝑥 − 6) cross the 𝑥-axis?

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Video Transcript

At which values of 𝑥 does the graph of the equation 𝑦 is equal to 𝑥 plus two multiplied by 𝑥 minus six cross the 𝑥-axis?

We know that any equation will intersect or cross the 𝑥-axis when 𝑦 is equal to zero. The quadratic equation 𝑦 is equal to 𝑥 plus two multiplied by 𝑥 minus six will cross the 𝑥-axis at two points as shown. This will happen when 𝑥 plus two multiplied by 𝑥 minus six is equal to zero. If the product of 𝑥 plus two and 𝑥 minus six equals zero, then either 𝑥 plus two equals zero or 𝑥 minus six equals zero. Subtracting two from both sides of the first equation gives us 𝑥 is equal to negative two. And adding six to both sides of the second equation gives us 𝑥 is equal to positive six or six.

The graph of the equation 𝑦 is equal to 𝑥 plus two multiplied by 𝑥 minus six crosses the 𝑥-axis when 𝑥 equals negative two or six. We can therefore conclude that the two values of 𝑥 are negative two and six.

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