Algebra 2 Final Review

Transformations

100

f(x)=x², and the transformation is g(x)=-x². How is this graph transformed?

It was flipped over the x-axis (down).

200

A quadratic function y=f(x) is plotted on a graph and the vertex of the resulting parabola is (-5, 3). What is the vertex of the function defined as g(x)=f(x-3)-5?

(-2,-2)

300

How is y=(-x)²-2 transformed from the function y=x²?

Flipped over y-axis and down 2

400

What type of transformation is happening to this function? 

f(x)=|x| to g(x)=-2|x+4|-3

Flipped over x-axis, shrink by x2, left 4 and down 3

500

What type of transformation is being done to this function:

f(x)= 2^x transfromed g(x)= -2^(-x+4)-6 

Flipped over x and y axis, left 4 and down 6.

Radicals

100

Write the expression in radical form:

x^3/4

4th root of x³

200

Simplify:

(100^1/2)⁵

100,000

300

Express 64^5/3 in simplest radical form.

1024

400

Simplify:

(27x⁹y^-6)^2/3

9x⁶/y⁴

500

Solve:

sqrt(x+13)=x+1

x=3,-4

Log and Exponentials

100

Is this a growth or decay and by how much?

y=99(1.03)^x

Growth, 3%

200

What is the value of log₃(81)?

4

300

Write the log equation as an exponential equation. 

log₉(x)=3x

9^3x=x

400

Solve for x.

25^x+2=5^x+3

x=-1

500

Solve for the exact value of x.

2ln(7x+4)-13=-1

(e⁶-4)/7

Problem Solving

100

What is 190% of 10?

19

200

What is the result when 70 is increased by 20%?

84

300

For Zoey's lemonade recipe, 7 lemons are required to make 14 cups of lemonade. At what rate are lemons being used in lemons per cup of lemonade?

1/2 lemons

400

Solve the system of equations:

3x+4y=6

-x-2y=2

(10,-6)

500

Given the speeds of each runner below, determine who runs the fastest.

Brooke runs 15 feet per second.

Jake runs 331 feet in 24 seconds.

Liz runs 1 mile in 428 seconds.

Frank runs 608 feet in 1 minute.

Brooke, 15 feet per second

Miscellaneous

100

Solve:

3x+2=5

x=1

200

what is the value of i²?

-1

300

Multiply and Simplify:

(5x-3)(x+4)

5x²+17x-12

400

What room are we in?

K-125

500

Solve the following system of equations for all three variables.

-5x-2y+z=-2

4x+8y+z=-10

6x-3y-z=-5

(-2,1,-10)