Algebra 2 Quadratic Equations Review Activity - Math Educational Resources | Ten Tors Math - Free Printable

It looks like you've uploaded an image containing a list of quadratic expressions labeled A through I. However, there is no specific task or question stated in the image — just the equations.

To help you properly, I’ll assume the intended task is one of the following common ones:

> "Factor each of the given quadratic expressions."

Let’s go through each expression and factor it (if possible). If factoring isn’t possible over integers, we'll note that.

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🔹 A: $ x^2 - 16x + 15 $

We need two numbers that multiply to +15 and add to -16.

- Factors of 15: (1,15), (3,5)
- Try: -1 and -15 → (-1) + (-15) = -16 ✔

So:
$$
x^2 - 16x + 15 = (x - 1)(x - 15)
$$

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🔹 B: $ x^2 + 2x - 15 $

Need two numbers that multiply to -15 and add to +2.

- Try: 5 and -3 → 5 × (-3) = -15, 5 + (-3) = 2 ✔

$$
x^2 + 2x - 15 = (x + 5)(x - 3)
$$

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🔹 C: $ 4x - x^2 - 13 $

Rewriting in standard form:
$$
-x^2 + 4x - 13
$$

Multiply by -1 to make leading coefficient positive:
$$
x^2 - 4x + 13
$$

Now check discriminant: $ D = (-4)^2 - 4(1)(13) = 16 - 52 = -36 < 0 $

No real roots → cannot factor over real numbers.

So original expression:
$$
4x - x^2 - 13 = -x^2 + 4x - 13 \quad \text{(Cannot be factored over reals)}
$$

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🔹 D: $ x^2 - 8x + 12 $

Need two numbers that multiply to 12, add to -8.

- Try: -6 and -2 → (-6)(-2)=12, (-6)+(-2)=-8 ✔

$$
x^2 - 8x + 12 = (x - 6)(x - 2)
$$

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🔹 E: $ 12x - x^2 - 35 $

Rewrite:
$$
-x^2 + 12x - 35
$$

Multiply by -1:
$$
x^2 - 12x + 35
$$

Find two numbers that multiply to 35, add to -12.

- Try: -7 and -5 → (-7)(-5)=35, (-7)+(-5)=-12 ✔

So:
$$
x^2 - 12x + 35 = (x - 7)(x - 5)
\Rightarrow -x^2 + 12x - 35 = -(x - 7)(x - 5)
$$

Or:
$$
E = -(x - 7)(x - 5)
$$

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🔹 F: $ x^2 - 8x + 15 $

Two numbers that multiply to 15, add to -8.

- Try: -5 and -3 → (-5)(-3)=15, (-5)+(-3)=-8 ✔

$$
x^2 - 8x + 15 = (x - 5)(x - 3)
$$

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🔹 G: $ x^2 - 6x + 12 $

Check discriminant:
$ D = (-6)^2 - 4(1)(12) = 36 - 48 = -12 < 0 $

No real roots → cannot factor over reals

So:
$$
x^2 - 6x + 12 \quad \text{does not factor over real numbers}
$$

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🔹 H: $ x^2 - 4x - 5 $

Need two numbers that multiply to -5, add to -4.

- Try: -5 and +1 → (-5)(1) = -5, (-5)+1 = -4 ✔

$$
x^2 - 4x - 5 = (x - 5)(x + 1)
$$

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🔹 I: $ x^2 + 7x + 10 $

Two numbers that multiply to 10, add to 7.

- Try: 5 and 2 → 5×2=10, 5+2=7 ✔

$$
x^2 + 7x + 10 = (x + 5)(x + 2)
$$

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## ✔ Final Factored Forms:

| Letter | Expression | Factored Form |
|--------|-----------------------------|-----------------------------------|
| A | $ x^2 - 16x + 15 $ | $ (x - 1)(x - 15) $ |
| B | $ x^2 + 2x - 15 $ | $ (x + 5)(x - 3) $ |
| C | $ 4x - x^2 - 13 $ | $ -x^2 + 4x - 13 $ → Not factorable over reals |
| D | $ x^2 - 8x + 12 $ | $ (x - 6)(x - 2) $ |
| E | $ 12x - x^2 - 35 $ | $ -(x - 7)(x - 5) $ |
| F | $ x^2 - 8x + 15 $ | $ (x - 5)(x - 3) $ |
| G | $ x^2 - 6x + 12 $ | Not factorable over reals |
| H | $ x^2 - 4x - 5 $ | $ (x - 5)(x + 1) $ |
| I | $ x^2 + 7x + 10 $ | $ (x + 5)(x + 2) $ |

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💡 Note: If your actual task was different (e.g., solve for x, graph, find vertex, etc.), please clarify, and I can adjust accordingly!

Let me know if you want to:
- Solve each equation set equal to zero,
- Find roots,
- Graph them,
- Or compare similarities.

But based on the information, factoring is the most likely intended task.