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.