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)

Answer 1

To find the x-intercepts of the function \( f(x) = x^2 + 4x - 12 \), we need to set the function equal to zero and solve for \( x \):

\[
x^2 + 4x - 12 = 0
\]

We can factor this quadratic equation. We are looking for two numbers that multiply to \(-12\) (the constant term) and add to \(4\) (the coefficient of the \(x\) term). The numbers \(6\) and \(-2\) work because:

\[
6 \times (-2) = -12
\]
\[
6 + (-2) = 4
\]

So we can factor the equation as:

\[
(x + 6)(x - 2) = 0
\]

Setting each factor to zero gives us the solutions:

1. \(x + 6 = 0 \) → \(x = -6\)
2. \(x - 2 = 0 \) → \(x = 2\)

Thus, the x-intercepts are at the points \((-6, 0)\) and \((2, 0)\).

The correct answer is:

\[
(-6, 0), (2, 0)
\]