Evaluating Quadratic Functions Worksheets - Free Printable

Let's solve each part of the worksheet step by step.

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A) Evaluate each function at the specified value.

#### 1) $ f(x) = (x + 3)^2 - 2x^2 $, $ x = -12 $

Substitute $ x = -12 $:

$$
f(-12) = (-12 + 3)^2 - 2(-12)^2
$$
$$
= (-9)^2 - 2(144)
$$
$$
= 81 - 288 = -207
$$

✔ Answer: -207

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#### 2) $ f(x) = -5x + 4x^2 $, $ x = -6 $

$$
f(-6) = -5(-6) + 4(-6)^2
$$
$$
= 30 + 4(36) = 30 + 144 = 174
$$

✔ Answer: 174

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B) Evaluate each function.

#### 1) $ f(x) = (3x - 14)^2 $, find $ f(11) $

$$
f(11) = (3(11) - 14)^2 = (33 - 14)^2 = (19)^2 = 361
$$

✔ Answer: 361

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#### 2) $ f(x) = -x^2 $, find $ f(-5) $

$$
f(-5) = -(-5)^2 = -(25) = -25
$$

✔ Answer: -25

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C) If $ f(x) = x^2 - 7x - 13 $, find the following.

#### 1) $ f(-15) $

$$
f(-15) = (-15)^2 - 7(-15) - 13 = 225 + 105 - 13 = 317
$$

✔ Answer: 317

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#### 2) $ f(12) $

$$
f(12) = (12)^2 - 7(12) - 13 = 144 - 84 - 13 = 47
$$

✔ Answer: 47

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#### 3) $ f(0) $

$$
f(0) = 0^2 - 7(0) - 13 = -13
$$

✔ Answer: -13

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#### 4) $ f(6) $

$$
f(6) = 6^2 - 7(6) - 13 = 36 - 42 - 13 = -19
$$

✔ Answer: -19

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D) If $ f(x) = (x - 2)^2 $, find the following.

#### 1) $ 4f(1) \times 6f(0) $

First, compute $ f(1) $ and $ f(0) $:

- $ f(1) = (1 - 2)^2 = (-1)^2 = 1 $
- $ f(0) = (0 - 2)^2 = (-2)^2 = 4 $

Now:
$$
4f(1) = 4 \times 1 = 4 \\
6f(0) = 6 \times 4 = 24 \\
\Rightarrow 4f(1) \times 6f(0) = 4 \times 24 = 96
$$

✔ Answer: 96

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#### 2) $ -8f(2) + 3f(4) $

Compute $ f(2) $ and $ f(4) $:

- $ f(2) = (2 - 2)^2 = 0^2 = 0 $
- $ f(4) = (4 - 2)^2 = 2^2 = 4 $

Now:
$$
-8f(2) = -8 \times 0 = 0 \\
3f(4) = 3 \times 4 = 12 \\
\Rightarrow -8f(2) + 3f(4) = 0 + 12 = 12
$$

✔ Answer: 12

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#### 3) $ -7f(7) + f(-8) $

Compute:

- $ f(7) = (7 - 2)^2 = 5^2 = 25 $
- $ f(-8) = (-8 - 2)^2 = (-10)^2 = 100 $

Now:
$$
-7f(7) = -7 \times 25 = -175 \\
f(-8) = 100 \\
\Rightarrow -175 + 100 = -75
$$

✔ Answer: -75

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#### 4) $ \frac{-3f(-1)}{f(5)} $

Compute:

- $ f(-1) = (-1 - 2)^2 = (-3)^2 = 9 $
- $ f(5) = (5 - 2)^2 = 3^2 = 9 $

Now:
$$
-3f(-1) = -3 \times 9 = -27 \\
\frac{-27}{f(5)} = \frac{-27}{9} = -3
$$

✔ Answer: -3

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E) What is the value of $ f(-3) $, if $ f(x) = 10x^2 + 8 $?

$$
f(-3) = 10(-3)^2 + 8 = 10(9) + 8 = 90 + 8 = 98
$$

So, $ f(-3) = 98 $

Now look at the options:

i) 91
ii) -88
iii) -96
iv) 98 ✔

✔ Answer: iv) 98

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✔ Final Answers Summary:

A)
1) -207
2) 174

B)
1) 361
2) -25

C)
1) 317
2) 47
3) -13
4) -19

D)
1) 96
2) 12
3) -75
4) -3

E) iv) 98

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