Question

Which of the following equivalent forms of the function f(x)=4x2+4x−24 is the most suitable to indicate the x-coordinates of the x‑intercepts of the graph of y=f(x) in the xy‑plane?

f(x)=4(x2+x−6)


f(x)=4(x−2)(x+3)


f(x)=2(x−2)(2x+6)


f(x)=(2x−4)(2x+6)

Answer 1

Explanation:

A: doesn't tell you anything except that 4 is a common factor. A is not the answer.

B looks like it is the answer. If you take out the common factor of 4, you get A. But A is not the answer as stated. But A factors further down.

f(X) = 4 (x^2 + x - 6)

The factors of 6 must be of the opposite sign because 6 is minus. It's factors are 3 and 2. The 3 is plus, the two is minus. So the answer is

f(x) = 4(x + 3)(x - 2). These will indicate the x intercepts. I've included a graph to show this. Notice that the actual intercepts are of the OPPOSITE sign.