Find out the x-intercepts & y-intercepts for each of the following equations.

                           y =x² +x - 6

Solution

As verification for each of these we will also sketch the graph of each of function. We will leave the details of the sketching to you to determine. 

                                                      y = x² + x - 6

Let's first determine the y-intercept(s).  Again, we do this by setting x = 0 & solving for y. usually this is the easier of the two.  Thus, let's determine the y-intercept(s).

                                y =(0)²  + 0 - 6 = -6

Thus, there is a single y-intercept : (0, -6) .

The work for the x-intercept(s) is approximately identical except in this case we set y = 0 and solve for x.  Following is that work.

0 =x² + x - 6

0 = (x + 3) (x - 2)

⇒         x =- 3, x = 2

For this equation there are two x-intercepts: (-3, 0) & (2, 0) . 

For verification reason here is sketch of the graph for this equation.