# Lesson 16

### Problem 1

For each equation, identify the values of $$a$$, $$b$$, and $$c$$ that you would substitute into the quadratic formula to solve the equation.

1. $$3x^2 + 8x + 4 = 0$$
2. $$2x^2 - 5x + 2 = 0$$
3. $$\text- 9x^2 + 13x - 1 = 0$$
4. $$x^2 + x - 11 = 0$$
5. $$\text- x^2 + 16x + 64 = 0$$

### Solution

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### Problem 2

Use the quadratic formula to show that the given solutions are correct.

1. $$x^2 + 9x + 20 =0$$. The solutions are $$x = \text- 4$$ and $$x = \text- 5$$.
2. $$x^2 - 10x + 21 = 0$$. The solutions are $$x = 3$$ and $$x = 7$$.
3. $$3x^2 - 5x + 1 = 0$$. The solutions are $$x = \frac56 \pm \frac{\sqrt{13}}{6}$$.

### Solution

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### Problem 3

Select all the equations that are equivalent to $$81x^2+180x-200=100$$

A:

$$81x^2+180x-100=0$$

B:

$$81x^2+180x+100=200$$

C:

$$81x^2+180x+100=400$$

D:

$$(9x+10)^2=400$$

E:

$$(9x+10)^2=0$$

F:

$$(9x-10)^2=10$$

G:

$$(9x-10)^2=20$$

### Solution

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(From Unit 7, Lesson 14.)

### Problem 4

Technology required. Two objects are launched upward. Each function gives the distance from the ground in meters as a function of time, $$t$$, in seconds.

Object A: $$f(t)=25+20t-5t^2$$

Object B: $$g(t)=30+10t-5t^2$$

Use graphing technology to graph each function.

1. Which object reaches the ground first? Explain how you know.
2. What is the maximum height of each object?

### Solution

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(From Unit 6, Lesson 6.)

### Problem 5

Identify the values of $$a$$, $$b$$, and $$c$$ that you would substitute into the quadratic formula to solve the equation.

1. $$x^2 + 9x + 18 = 0$$
2. $$4x^2 - 3x + 11 = 0$$
3. $$81 - x + 5x^2 = 0$$
4. $$\frac45 x^2 + 3x = \frac13$$
5. $$121 = x^2$$
6. $$7x + 14x^2 = 42$$

### Solution

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### Problem 6

On the same coordinate plane, sketch a graph of each function.

• Function $$v$$, defined by $$v(x) = |x+6|$$
• Function $$z$$, defined by $$z(x)= |x|+9$$

### Solution

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(From Unit 4, Lesson 14.)