Solving Quadratic Equations, (By Factoring), Coloring Activity - Free Printable

It looks like you've uploaded an image of a "Solving Quadratic Equations by Factoring" coloring activity worksheet created by All Things Algebra®. The activity combines algebra practice with a fun coloring component.

However, the quadratic equations on the left side are cut off, so I can't see the full expressions or the answer choices needed to solve them. But based on the visible parts and the typical structure of such worksheets, I can explain how this type of activity works and guide you through solving quadratic equations by factoring—which is likely what's required here.

---

🔍 How This Activity Works:

1. Solve each quadratic equation by factoring.
2. Find the correct solutions (roots) for each equation.
3. Use the solution(s) to determine which color to use for the corresponding number in the beach scene.
4. Color the sections labeled with that number using the matching color code.

For example:
- If the solution to problem #1 is `x = -2` and `x = -8`, and the key says "color all sections with 1 → yellow", then you'd color the parts labeled "1" in yellow.

---

✔ Step-by-Step: Solving Quadratics by Factoring

Let’s assume some common types of problems that might appear (since the actual ones are partially obscured). Here’s how to solve them:

#### Example 1: $ x^2 + 10x + 24 = 0 $
We need two numbers that multiply to 24 and add to 10.
- Factors of 24: (1,24), (2,12), (3,8), (4,6)
- 4 and 6 → 4×6=24, 4+6=10 ✔
So:
$$
x^2 + 10x + 24 = (x + 4)(x + 6) = 0
\Rightarrow x = -4, -6
$$

#### Example 2: $ x^2 - 7x + 12 = 0 $
Need two numbers that multiply to 12 and add to -7.
- -3 and -4 → (-3)(-4)=12, (-3)+(-4)=-7 ✔
$$
(x - 3)(x - 4) = 0 \Rightarrow x = 3, 4
$$

#### Example 3: $ 2x^2 - 12x = 0 $
Factor out GCF first:
$$
2x(x - 6) = 0 \Rightarrow x = 0, 6
$$

#### Example 4: $ x^2 + 8x + 15 = 0 $
Need numbers that multiply to 15 and add to 8 → 3 and 5
$$
(x + 3)(x + 5) = 0 \Rightarrow x = -3, -5
$$

#### Example 5: $ x^2 - 5x - 14 = 0 $
Factors of -14: (1,-14), (-1,14), (2,-7), (-2,7)
→ -7 and 2: (-7)(2) = -14, (-7)+2 = -5 ✔
$$
(x - 7)(x + 2) = 0 \Rightarrow x = 7, -2
$$

#### Example 6: $ 3x^2 + 13x + 4 = 0 $
Use AC method: A=3, C=4 → AC=12
Find factors of 12 that add to 13: 1 and 12
Split middle term:
$$
3x^2 + 12x + x + 4 = 3x(x + 4) + 1(x + 4) = (3x + 1)(x + 4)
\Rightarrow x = -\frac{1}{3}, -4
$$

#### Example 7: $ x^2 + 5x + 6 = 0 $
→ (x + 2)(x + 3) = 0 → x = -2, -3

---

🎨 Coloring Instructions (Typical Format):

After solving each equation, match the solution(s) to a color key (not visible in your image). For instance:

| Answer | Color |
|--------|-------|
| x = -2, -3 | Blue |
| x = 0, 6 | Green |
| x = -4, -6 | Orange |

Then, color all regions labeled with the problem number using the corresponding color.

---

❗ Important Note:

Since the equations are incomplete in your image (e.g., only "$x^2 + 10x$" is shown — missing constant term), I cannot solve the exact problems without seeing the full equations.

---

✔ What You Should Do:

1. Complete the equations from your original worksheet (likely printed).
2. Solve each one by factoring.
3. Match answers to a color key provided on the sheet.
4. Color the beach scene accordingly.

---

💡 Tips for Success:

- Always set the equation equal to zero first.
- Factor completely.
- Use the Zero Product Property: if $ ab = 0 $, then $ a = 0 $ or $ b = 0 $.
- Check your solutions by plugging back into the original equation.

---

If you can share the full list of equations or the answer key, I’d be happy to help solve them step-by-step and guide you through the coloring! 😊