Question

Directions: Use this worksheet to record your answers to the questions or
problems for the Graphs of Polynomials portfolio. When you are finished, save this
worksheet with your answers and submit it for a portfolio grade.
Where indicated, draw figures on a blank sheet of paper or on a sheet of graph paper.
Be sure to label each sheet so that your teacher knows which answer goes with which
question. You can scan these figures and submit them as individual documents with
your portfolio worksheet, or you can take pictures of them and insert the pictures on
the portfolio worksheet.
Finding the Zeros of a Polynomial Function
Question 1
A. Choose whole numbers to fill in the two blanks in the following polynomial
function:
h(x) =-3x^2(5x+----------)(x-)
B. Find the zeros of h(x). Show your work.
C. Plot the zeros of h(x) on a coordinate plane on a piece of graph paper. Label
this paper Graph 1.
Note: You will complete Graph 1 throughout the portfolio. Do not worry about
scaling the y-axis at this time

Answer 1

### Finding the Zeros of a Polynomial Function

#### Question 1

**A. Choose whole numbers to fill in the two blanks in the following polynomial function:**

Let’s fill in the blanks with whole numbers. For example:
- Let’s use **3** in the first blank.
- Let’s use **4** in the second blank.

So, the polynomial function becomes:

**h(x) = -3x^2(5x + 3)(x - 4)**

---

**B. Find the zeros of h(x). Show your work.**

To find the zeros of the polynomial function, we need to set \( h(x) = 0 \):

\[
-3x^2(5x + 3)(x - 4) = 0
\]

This equation equals zero if any of the factors are equal to zero.

1. **From \( -3x^2 = 0 \):**
\[
x^2 = 0 \quad \Rightarrow \quad x = 0
\]

2. **From \( 5x + 3 = 0 \):**
\[
5x = -3 \quad \Rightarrow \quad x = -\frac{3}{5}
\]

3. **From \( x - 4 = 0 \):**
\[
x = 4
\]

**Thus, the zeros of \( h(x) \) are:**
- \( x = 0 \)
- \( x = -\frac{3}{5} \) (which is approximately -0.6)
- \( x = 4 \)

---

**C. Plot the zeros of h(x) on a coordinate plane on a piece of graph paper. Label this paper Graph 1.**

To plot these zeros on a coordinate plane:

1. **Plot the zero at \( x = 0 \)** (the origin of the graph).
2. **Plot the zero at \( x = -\frac{3}{5} \)** (approximately -0.6 on the x-axis).
3. **Plot the zero at \( x = 4 \)** (to the right on the x-axis).

Make sure to clearly label each point on the graph with its corresponding zero. After plotting, the graph will visually represent the zeros of the polynomial function \( h(x) \).

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### Submission

- Ensure you have labeled your graph as **Graph 1**.
- Save your answers and the graph with its label.
- Submit the portfolio worksheet along with the scanned graph or picture as required.

If you need any more help with this or further questions, feel free to ask!