Question Video: Determining Where the Graph of a Quadratic Equation in Two Variables in Factored Form Crosses the 𝑥-Axis | Nagwa Question Video: Determining Where the Graph of a Quadratic Equation in Two Variables in Factored Form Crosses the 𝑥-Axis | Nagwa

Question Video: Determining Where the Graph of a Quadratic Equation in Two Variables in Factored Form Crosses the 𝑥-Axis Mathematics • First Year of Secondary School

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At which values of 𝑥 does the graph of the equation 𝑦 = (3𝑥 − 2)(𝑥 + 1) 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 three 𝑥 minus two multiplied by 𝑥 plus one cross the 𝑥-axis?

We know that any equation crosses the 𝑥-axis when 𝑦 is equal to zero. In this question, we have a U-shaped quadratic graph that will cross the 𝑥-axis at two distinct points. These will occur when three 𝑥 minus two multiplied by 𝑥 plus one is equal to zero. For this to be true, one of our parentheses must equal zero. Either three 𝑥 minus two equals zero or 𝑥 plus one is equal to zero.

For our first equation, we can begin by adding two to both sides. We then divide both sides of the equation by three, giving us 𝑥 is equal to two-thirds. For the second equation, we simply subtract one from both sides such that 𝑥 is equal to negative one. This means that our quadratic graph crosses the 𝑥-axis at values of 𝑥 equal to negative one and two-thirds. These are the two correct answers to this question.

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