Consider the function f (x) = x2 + 12x + 11. x-intercepts?

The x-intercepts of this function are - 11 and - 1.

The easiest way to find the intercepts of this graph is by factoring. To factor a quadratic, we look for factors of the last number, that add up to the middle number. Below are the factors of the last number.

1 and 11

-1 and - 11

Now we look for one that adds up to positive 12.

1 and 11

-1 and - 11

Since these two add up to the middle number, we can use them in parenthesis with x + and factor. If there was not a pair, we would then have to use the quadratic equation.

f (x) = (x + 1) (x + 11)

Now to solve for the x-intercepts, we set each parenthesis equal to 0 and solve for x.

x + 1 = 0

x = - 1

x + 11 = 0

x = - 11