# Lesson 16

• Let’s learn a formula for finding solutions to quadratic equations.

### 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. $$\text- x^2 + 16x + 64 = 0$$

### 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 $$x = \frac56 \pm \frac{\sqrt{13}}{6}$$.

### 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:

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

(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?
(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. $$7x + 14x^2 = 42$$

### 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 $$z(x)= |x|+9$$