https://file.aiquickdraw.com/mathbot/file/1729315743407tke6hy8o.jpg

The function given in the image is:

\[
f(x) = (x + 3)(x - 5)
\]

### 1) **What are the zeros of the function?**
To find the zeros of the function, set \( f(x) = 0 \) and solve for \(x\):
\[
(x + 3)(x - 5) = 0
\]
This gives us two solutions:
\[
x + 3 = 0 \quad \Rightarrow \quad x = -3
\]
\[
x - 5 = 0 \quad \Rightarrow \quad x = 5
\]

So, the zeros (or roots) of the function are:
- Smaller \(x = -3\)
- Larger \(x = 5\)

### 2) **What is the vertex of the parabola?**
Since the function is in factored form, we can find the x-coordinate of the vertex as the midpoint of the two zeros:
\[
x_{\text{vertex}} = \frac{-3 + 5}{2} = \frac{2}{2} = 1
\]

To find the y-coordinate of the vertex, substitute \(x = 1\) into the function:
\[
f(1) = (1 + 3)(1 - 5) = 4 \times (-4) = -16
\]

Thus, the vertex of the parabola is:
\[
(1, -16)
\]

---

Would you like further clarification or additional details on any part of this? Below are some follow-up questions for deeper exploration:

1. How would the graph of the function \(f(x) = (x+3)(x-5)\) look like?
2. How can we rewrite the function \(f(x)\) in standard quadratic form?
3. What is the axis of symmetry for this parabola?
4. How can you find the y-intercept of this function?
5. What does the negative value of the vertex's y-coordinate indicate about the graph?

**Tip:** The zeros of a quadratic function always help determine where the parabola intersects the x-axis.

Given the function f(x) = (x + 3)(x - 5), find the zeros of the function and the vertex of the parabola.

Explore how to find the zeros and vertex of the quadratic function f(x) = (x + 3)(x - 5). This step-by-step guide covers key concepts in algebra, including solving quadratic equations and using the midpoint formula to determine the vertex of a parabola. Suitable for Grades 8-10.

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