Unit 3 review

Quadratic solutions

100

Solve the following equation. HINT: There may be more than one answer.

x^2=169

x = 13 or x = -13

200

Solve the following equation. HINT: There may be more than one answer.

x^2-1=99

x^2-1+1=99+1

x^2=100

x=10 or x=-10

300

Solve the following equation. HINT: There may be more than one answer.

x(x+2)=24

4(6)=24 and -6(-4)=24

x=4 or x=-6

Quadratic formula

100

Solve the function using the quadratic formula. You do NOT need to simplify your answers.

4x^2-5x-12=0

x=(-(-5)+-sqrt((-5)^2-4(4)(-12)))/(2(4))

x in {-1.21636,2.46636}

200

Solve the function using the quadratic formula. You do NOT need to simplify your answers.

x^2-5x+6=0

x=(-(-5)+-sqrt((-5)^2-4(1)(6)))/(2(1))

x in {2,3}

300

Solve the function using the quadratic formula. You do NOT need to simplify your answers.

3x^2+4x=2

3x^2+4x-2=0

x=(-4+-sqrt(4^2-4(3)(-2)))/(2(3))

x in {-1.721,0.387}

Exponential solutions

100

Solve the following equation.

3^x=27

Method 1:

3^3=27=>x=3

Method 2:

log_3(3^x)=log_3(27)

x=(log(27))/log(3)=3

200

Solve the following equation.

2^x/4=4

2^x/4(4)=4(4)

2^x=16

log_2(2^x)=log_2(16)

x=4

300

Solve the following equation.

2^(x+3)=64

log_2(2^(x+3))=log_2(64)

x+3=6

x=3

Expo <-> Log

100

Rewrite the following equation in logarithmic form.

9^x=1

log_9(1)=x

200

Rewrite the following equation in exponential form.

log_8(x)=1/2

8^(1/2)=x

300

At your tables, write an exponential equation and a logarithmic equation that are equivalent.

Many answers possible :)

Solving vs. evaluating

100

EVALUATE the function f(x) when x = 5. SOLVE for x when f(x) = 5.

f(x)=8x+3

Evaluation:

f(5)=8(5)+3=43

Solving:

5=8x+3=>2=8x=>x=0.25

200

Is the following problem an example of evaluation or solving?

"The function f(x) = 18000(0.9901)^x represents the depreciation of a car's value after x years. Find the price of the car after 5 years."

Evaluation

300

Is the following problem an example of evaluation or solving?

"The function f(x) = 18000(0.9901)^x represents the depreciation of a car's value after x years. After how many years is the car worth half of its original value?"

Solving

Potpourri

100

According to the Merriam-Webster dictionary, when was the term “Friendsgiving” first widely used?

2007

200

In what year was Thanksgiving first recognized as a national holiday?

1863 (under Pres. Abraham Lincoln)

300

What is the name of the Indigenous nation that formed diplomatic treaties and political alliances with English colonial settlers in 1620?

Wampanoag or Wôpanâak