Question

what are the x-intercepts of the graph of the function f(x) = x² + 4x − 12? (-6, 0), (2,0) (-2, -16), (0, -12) (-6, 0), (-2, -16), (2, 0) (0, -12), (-6, 0), (2, 0)

Explanation:

Step1: Recall x-intercept definition

x-intercepts occur where \( y = 0 \), so we solve \( f(x)=x^{2}+4x - 12 = 0 \).

Step2: Factor the quadratic

Factor \( x^{2}+4x - 12 \). We need two numbers that multiply to -12 and add to 4. These numbers are 6 and -2. So, \( x^{2}+4x - 12=(x + 6)(x - 2) \).

Step3: Solve for x

Set each factor equal to zero: \( x + 6 = 0 \) gives \( x=-6 \); \( x - 2 = 0 \) gives \( x = 2 \). Thus, the x-intercepts are \( (-6,0) \) and \( (2,0) \). We can also check the graph: the parabola crosses the x-axis at \( x=-6 \) and \( x = 2 \), so the points are \( (-6,0) \) and \( (2,0) \).

Answer:

A. \((-6, 0), (2,0)\)