To solve for the x-intercepts of the quadratic function $y = x^2 + 4x - 32$, we need to find the values of $x$ where $y = 0$. This involves solving the quadratic equation:

$x^2 + 4x - 32 = 0$

To solve this, we can factor the quadratic equation.

1. We need to find two numbers that multiply to $-32$ (the constant term) and add up to $4$ (the coefficient of the $x$ term).

   The numbers $8$ and $-4$ satisfy these conditions because: $8 \times (-4) = -32 \quad \text{and} \quad 8 + (-4) = 4$

2. We can now factor the quadratic equation as: $(x + 8)(x - 4) = 0$

3. To find the x-intercepts, set each factor equal to zero and solve for $x$: $x + 8 = 0 \quad \Rightarrow \quad x = -8$ $x - 4 = 0 \quad \Rightarrow \quad x = 4$

Thus, the x-intercepts are $(-8, 0)$ and $(4, 0)$.

Correct Answer:

The correct option is B. $(-8, 0)$ and $(4, 0)$.

Would you like more details on this solution or have any questions?

Here are 5 related questions you could explore next:

1. How do you derive the quadratic formula, and when should you use it?
2. What is the significance of the discriminant in a quadratic equation?
3. How can you use the vertex form of a quadratic equation to find the x-intercepts?
4. What are the possible types of solutions (real or complex) for a quadratic equation?
5. How do you complete the square to solve a quadratic equation?

Tip: When solving quadratic equations, factoring is often the quickest method if the equation can be easily factored, but the quadratic formula is a reliable method when factoring is complex or not possible.