# Lesson 14

Completing the Square (Part 3)

### Problem 1

Select all expressions that are perfect squares.

A:

$$9x^2 + 24x + 16$$

B:

$$2x^2 + 20x + 100$$

C:

$$(7 - 3x)^2$$

D:

$$(5x + 4)(5x - 4)$$

E:

$$(1 - 2x)(\text- 2x + 1)$$

F:

$$4x^2 + 6x + \frac94$$

### Solution

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### Problem 2

Find the missing number that makes the expression a perfect square. Next, write the expression in factored form.

1. $$49x^2 - \underline{\hspace{.5in}} x + 16$$
2. $$36x^2 + \underline{\hspace{.5in}} x + 4$$
3. $$4x^2 - \underline{\hspace{.5in}} x + 25$$
4. $$9x^2 + \underline{\hspace{.5in}} x + 9$$
5. $$121x^2 + \underline{\hspace{.5in}} x + 9$$

### Solution

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### Problem 3

Find the missing number that makes the expression a perfect square. Next, write the expression in factored form.

1. $$9x^2 + 42x + \underline{\hspace{.5in}}$$
2. $$49x^2 - 28x +\underline{\hspace{.5in}}$$
3. $$25x^2 + 110x + \underline{\hspace{.5in}}$$
4. $$64x^2 - 144x +\underline{\hspace{.5in}}$$
5. $$4x^2 + 24x + \underline{\hspace{.5in}}$$

### Solution

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### Problem 4

1. Find the value of $$c$$ to make the expression a perfect square. Then, write an equivalent expression in factored form.
standard form $$ax^2+bx+c$$ factored form $$(kx+m)^2$$
$$4x^2+4x$$
$$25x^2-30x$$
2. Solve each equation by completing the square.

$$4x^2+4x=3$$

$$25x^2-30x+8=0$$

### Solution

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### Problem 5

For each function $$f$$, decide if the equation $$f(x)=0$$ has 0, 1, or 2 solutions. Explain how you know.

### Solution

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(From Unit 7, Lesson 5.)

### Problem 6

Solve each equation.

$$p^2+10=7p$$

$$x^2+11x+27=3$$

$$(y+2)(y+6)=\text-3$$

### Solution

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(From Unit 7, Lesson 9.)

### Problem 7

Which function could represent the height in meters of an object thrown upwards from a height of 25 meters above the ground $$t$$ seconds after being launched?

A:

$$f(t)=\text-5t^2$$

B:

$$f(t)=\text-5t^2+25$$

C:

$$f(t)=\text-5t^2+25t+50$$

D:

$$f(t)=\text-5t^2+50t+25$$

### Solution

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(From Unit 6, Lesson 6.)

### Problem 8

A group of children are guessing the number of pebbles in a glass jar. The guesses and the guessing errors are plotted on a coordinate plane.

1. Which guess is furthest away from the actual number?
2. How far is the furthest guess away from the actual number?

### Solution

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(From Unit 4, Lesson 13.)