Exercise 88 Page 447

We can use any of the following methods to find how many times the graph intersects the x-axis.

• Quadratic Formula
• Zero Product Property
• Completing the square

Let's use the Quadratic Formula and the completing the square for this problem.

Quadratic formula

To use the Quadratic Formula, we have to equate y with 0.

Completing the Square

Given the solutions from the Quadratic Formula, we should not use the zero product property as the zeroes are not integers. Instead we will complete the square. To complete the square, we equate y with 0 and then rewrite it in the following format. x^2+bx=c Let's start by doing this.

Next we will rewrite the left-hand side so that it can be written as a square. To do that, we have to add the square of half the coefficient to x, which is ( 1.42)^2=0.7^2, to both sides of the equation. This is called completing the square.

Both methods gives the same answer.