https://file.aiquickdraw.com/mathbot/file/1727403849579tvkzg0mx.jpg

Let's solve the problem from the image:

The function given is:
\[ f(x) = x^2 + x - 42 \]

### Step 1: Factor the quadratic equation.
We need to factor this expression. To factor it, find two numbers that multiply to \(-42\) (the constant term) and add up to \(1\) (the coefficient of the middle term, \(x\)).

The numbers \(7\) and \(-6\) satisfy this condition because:
\[ 7 \times (-6) = -42 \]
\[ 7 + (-6) = 1 \]

So, the factored form is:
\[
f(x) = (x + 7)(x - 6)
\]

### Step 2: Solve for the zeros (x-intercepts).
To find the x-intercepts (or zeros), set each factor equal to zero:
\[
x + 7 = 0 \quad \text{or} \quad x - 6 = 0
\]
Solve these equations:
\[
x = -7 \quad \text{or} \quad x = 6
\]

### Conclusion:
The x-intercepts are \(x = -7\) and \(x = 6\).

Now, looking at the answer options:
- **B** is correct because the zeros and the x-intercepts are the same: \(-7\) and \(6\).

Would you like more details or have any questions?

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Here are 5 follow-up questions you could explore:
1. What do the x-intercepts represent graphically?
2. How would you find the vertex of this quadratic function?
3. What is the axis of symmetry for this quadratic equation?
4. How can you confirm the factorization by expanding the factors back?
5. How does the discriminant help determine the nature of the roots?

**Tip:** Whenever factoring quadratics, always check the product and sum of the factors to ensure accuracy.

Find the zeros of the quadratic function by factoring. What are the x-intercepts of the graph of the function? F(x) = x^2 + x - 42

Learn how to factor the quadratic equation F(x) = x^2 + x - 42 to find the zeros and x-intercepts. This detailed solution demonstrates the factoring process and applies the zero-product property, ideal for students in grades 8-10.

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