What are the x intercepts of the graph of the function f(x) = x² + 4x – 12?

To find the x-intercepts of the function f(x) = x² + 4x – 12, we need to set the function equal to zero and solve for x.

So, we start with:

x² + 4x - 12 = 0

This is a quadratic equation, which we can solve by factoring, completing the square, or using the quadratic formula. In this case, let’s try factoring.

We look for two numbers that multiply to -12 (the constant term) and add to 4 (the coefficient of the x term). These numbers are 6 and -2.

Thus, we can factor the equation as:

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

Next, we set each factor equal to zero:

x + 6 = 0  
x - 2 = 0

Solving these gives us:

x = -6  
 x = 2

So, the x-intercepts of the graph are at the points (-6, 0) and (2, 0). This means the graph crosses the x-axis at these two points.