what are the x - intercepts of the graph of the function ( f(x)=x^{2}+4x - 12 )?\n( (-6,0),(2,0) )\n(…

what are the x - intercepts of the graph of the function ( f(x)=x^{2}+4x - 12 )?\n( (-6,0),(2,0) )\n( (-2,-16),(0,-12) )\n( (-6,0),(-2,-16),(2,0) )\n( (0,-12),(-6,0),(2,0) )

what are the x - intercepts of the graph of the function ( f(x)=x^{2}+4x - 12 )?\n( (-6,0),(2,0) )\n( (-2,-16),(0,-12) )\n( (-6,0),(-2,-16),(2,0) )\n( (0,-12),(-6,0),(2,0) )

Answer

Explanation:

Step1: Find x - intercepts

Set (f(x)=0), so (x^{2}+4x - 12=0).

Step2: Factor the quadratic equation

We need two numbers that multiply to (-12) and add up to (4). The numbers are (6) and (-2). So, (x^{2}+4x - 12=(x + 6)(x - 2)=0).

Step3: Solve for x

Using the zero - product property: If (x+6 = 0), then (x=-6). If (x - 2=0), then (x = 2).

Answer:

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