Algebra 2

5. A Major League Baseball stadium sells three types of tickets. Reserved tickets are sold for $20 each, field-level tickets are sold for $50 each, and box seat tickets are sold for $100 each. You purchase 10 total tickets for $370. You have twice as many reserved tickets as field-level tickets. How many tickets of each do you have?

Write a function g whose graph represents the indicated transformation of the graph of f.

6. f(x) = 4x + 1; translation 2 units left

7. f(x) = -4|x - 2|; vertical shrink by a factor of 1/2

8. Let g be a translation 4 units down and a horizontal shrink by a factor of 1/4 of the graph of f(x) = x

9. Let g be a reflection in the x-axis and a vertical stretch by a factor of 3, followed by a translation 4 units down and 1 unit right of the graph of f(x) = |x|

10. The total reimbursement (in dollars) for driving a company car m miles can be modeled by the function f(x) = 0.45m + 5. After a policy change, five more dollars are added on and then the total reimbursement amount is multiplied by 1.25. Describe how to transform the graph of f. What is the total reimbursement for a trip of 95 miles?

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Unit 2 - Quadratic Functions

Terms to Know

Terms to Know:

axis of symmetry
directrix
focus
intercept form
maximum value
minimum value
parabola
quadratic function
standard form
vertex form
vertex of a parabola

Notes: 10 Bullet Points from each section or 3-5 sentence summaries from each section.

Section 2.1: Transformations of Quadratic Functions

Section 2.2: Characteristics of Quadratic Functions

Section 2.3: Focus of A Parabola

Section 2.4: Modeling with Quadratic Functions

Important Questions: Answer the following Questions

1. A parabola has an axis of symmetry y = -4 and passes through the point (2, -1). Find another point that lies on the graph of the parabola.

2. Let the graph of g be a horizontal shrink by a factor of 1/3, followed by a translation 1 unit up of the graph of f(x) = x². Write a rule for g.

3. Let the graph of g be a translation 2 units up and 2 units right, followed by a reflection in the y-axis of the graph of f(x) = -(x + 3)². Write a rule for g.

4. Identify the focus, directrix, and axis of symmetry of x = -(1/20)y².

Write a rule for g and identify the vertex.

5. Let g be a translation 2 units up, followed by a reflection in the x-axis and a vertical stretch by a factor of 4 of the graph of f(x) = x²

6. Let g be a horizontal shrink by a factor of 1/3, followed by a translation 2 units up and 4 units left of the graph of f(x) = (3x - 2)² + 5

Find the x-intercepts of the graph of the function. Then describe where the function is increasing and decreasing.

7. g(x) = -1(x - 4)(x + 2)

8. g(x) = (1/4)(x - 6)(x - 3)

9. An object is launched directly overhead at 36 meters per second. The height (in meters) of the object is given by h(t) = -16t² + 36t + 5, where t is the time (in seconds) since the object was launched. For how many seconds is the object at or above a height of 25 meters?

10. A model rocket is launched from the top of a building. The height (in meters) of the rocket above the ground is given by h(t) = -6t² +24t +14, where t is the time (in seconds) since the rocket was launched. What is the rocket’s maximum height?

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Unit 3 - Quadratic Equations and Complex Numbers

Terms to Know

Terms to Know:

completing the square
complex number
discriminant
imaginary number
imaginary unit i
pure imaginary number
quadratic equation in one variable
Quadratic Formula
quadratic inequality in one variable
quadratic inequality in two variables
root of an equation
system of nonlinear equations
zero of a function

Notes: 10 Bullet Points from each section or 3-5 sentence summaries from each section.

Section 3.1: Solving Quadratic Equations

Section 3.2: Complex Numbers

Section 3.3: Completing The Square

Section 3.4: Using The Quadratic Formula

Section 3.5: Solving Nonlinear Systems

Section 3.6: Quadratic Inequalities

Important Questions: Answer the following Questions

Solve the equation using any method.

x² + 12x + 35 = 0
3x² - 48 = 0
x² + 10x + 25 = 64
-3x² - 5x = 5
4x² + 3x - 10 = 0
36x² + 49 = 0
A golf ball is hit from the ground, and its height can be modeled by the equation h(t) = -16t² + 128t, where h(t) represents the height (in feet) of the ball t seconds after contact. What will the maximum height of the ball be?
Write (1 - i) - (4 - 5i) as a complex number in standard form.
Write (-4 + 5i)(5 - i) as a complex number in standard form.
A company that produces video games has hired you to set the sale price for its newest game. Based on production costs and consumer demand, the company has concluded that the equation p(x) = -0.3x² + 45x - 1000 represents the profit p (in dollars) for x individual games sold. What will the company’s profit be if it sells 100 games?

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Unit 4 - Polynomial Functions

Terms to Know

Terms to Know:

complex conjugates
end behavior
even function
factor by grouping
factored completely
finite differences
local maximum
local minimum
odd function
Pascal’s Triangle
polynomial
polynomial function
polynomial long division
quadratic form
repeated solution
synthetic division

Notes: 10 Bullet Points from each section or 3-5 sentence summaries from each section.

Section 4.1: Graphing Polynomial Equations

Section 4.2: Adding, Subtracting, and Multiplying Polynomials

Section 4.3: Dividing Polynomials

Section 4.4: Factoring Polynomials

Section 4.5: Solving Polynomial Equations

Section 4.6: The Fundamental Theorem of Algebra

Section 4.7: Transformations of Polynomial Functions

Section 4.8: Analyzing Graphs of Polynomial Functions

Section 4.9: Modeling With Polynomial Functions

Example 1

Example 2

Example 3

Important Questions: Answer the following Questions

Perform the indicated operation.

(2x - 2)²
(c⁸ - 6)(c² - 4c - 2)
(4x³ + 20x² + 12x - 16) / (x - 4)
(b + 3)(b + 3)(b + 2)
(3x⁴ - 2x³ + 5x - 3) / (x² - 3x + 1)
(3x + 1)³
(5x² - 2) - (4x² + 6x - 4)

Factor the polynomial completely.

4a² - 12a + 8
5x⁴ - 80
2z³ - 3z² + 4z - 3

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Unit 5 - Rational Exponents and Radical Functions

Terms to Know

Terms to Know:

conjugate
extraneous solutions
index of a radical
inverse functions
like radicals
nth root of a
radical equation
radical function
simplest form

Notes: 10 Bullet Points from each section or 3-5 sentence summaries from each section.

Section 5.1: nth Roots and Rational Exponents

Section 5.2: Properties of Rational Exponents and Radicals

Section 5.3: Graphing Radical Functions

Section 5.4: Solving Radical Equations and Inequalities

Section 5.5: Performing Function Operations

Section 5.6: Inverse of A Function

Important Questions: Answer the following Questions

Simplify the expression.

(-32)^3/5
27²^/³
(-8x³y⁵z⁷)¹^/3

Find the real solution(s) of the equation. Round your answer to two decimal places.

3x⁵ = 3072
(x + 5)³ = 50
Write two functions whose graphs are translations of the graph y = x^1/². The first function should have a domain of x >= -3.

The second function should have a range of y <= 3.

The equation d = (1.35h)^1/2 represents the distance d (in miles) you can see out into the horizon, where h is the height (in feet) of your eyes above ground level. Determine how tall a person is if he or she can see 2.75 miles out into the horizon. Round your answer to the nearest hundredth.
Solve the inequality 6(x - 2)^1/2 + 4 <= 28 and the equation 6(x - 2)^1/2 + 4 = 28. Describe a similarity and a difference between solving radical equations and inequalities.

The total number of months m that it takes to produce p tennis rackets (in thousands) is given by the formula m = p³/90.

Find the inverse of the function.
How many tennis rackets will be produced in 20 months? Round your answer to the nearest whole tennis racket.

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