Find out the x-intercepts & y-intercepts for each of the following equations.
y =x^{2} +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 = x^{2} + 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 =x^{2} + 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.