Chapter 1:
Lesson
Exercise
Graph Quadratic Functions
in Standard Forms
What is the effect on the graph of the function
y = x2 when it is changed to y = –2x2 + 3?
Graph Quadratic Functions
in Vertex or Intercept
Form
Write the quadratic function
y = –2(x – 1)(x + 3) in standard
form. Give the vertex, axis of symmetry, and xintercepts. Is the vertex a maximum or
minimum point?
Solve x2 + bx + c = 0 by
Factoring
Find the zeros of the function y = x2 + 10x – 24
by rewriting the function in intercept form.
Explain what this tells you about the graph of
the function.
Solve ax2 + bx + c = 0 by
Factoring
A rectangular rug has an area of 15 square
units. It measures 4x + 5 units long and x + 4
units wide. Find the value of x.
Solve Quadratic Equations
by Finding Square Roots
Perform Operations with
Complex Numbers
Write the expression as a complex number in
standard form.
(2 – 5i)(–3 + 9i)
Complete the Square
Solve 6x2 + 10x – 55 = x2 + 100 by completing
the square. What does this tell you about the
graph of y = 5x2 + 10x – 155?
Use the Quadratic Formula
and the Discriminant
KEY IDEAS/Essential Questions/Formulas/etc.
Graph the function. Label the vertex and the axis of symmetry.
1. y = –2x2
2. g(x) =
3 2
9
x  3x 
4
4
10. A wilderness park is approximately 1 mile wide by 20 miles long. A
large expansion project is underway that will give the park 6 times its
current area. The same distance x will be added to the width and the
length. Write and solve an equation to find the value of x. What will
the dimensions of the park be after the expansion project?
Find the zeros of the function by rewriting in intercept form.
11. f(x) = 2x2 – 4x
12. y = 2x2 – 11x – 21
13. Simplify 6• 12 • 6 • 2.
Solve the equation.
3. A thrown ball hits the ground and bounces along a parabolic path
2
52
320
given by y =  x 2  x 
where x is measured in feet.
9
9
9
What is the maximum height that the ball reaches on this bounce?
Graph the function. Label the vertex and the axis of symmetry.
For Exercise 5, also label the x–intercepts.
4. y =
1
(x + 1)2 – 2
2
5. y = –2(x – 1)(x – 2)
14. 25x2 = 16
15. x2 – 3x + 5 = 0
1  3i
as a complex number in standard form.
2  5i
17. Find the absolute value of 5 – 12i.
16 Write
18. Write (3 – 2i) – (–11 – 9i) as a complex number in standard form.
Solve the equation by completing the square
19. x2 + 9x + 9 = 0
20. 3w2 – 7w + 19 = 0
21. An online retailer sells songs for $1. At this rate, they sell about
3000 songs per hour. For each $.10 decrease in price, they sell
about 500 more songs. The retailer’s revenue can be modeled by
R = (1 – 0.1x)(3000 + 500x). Use the vertex form to find how the
store can maximize hourly revenue.
22. Solve r2 = 18 – 7r.
6. Tell whether y = –3(x + 1)2 + 4 has a minimum value or a
maximum value. Then find that value.
Factor the expression.
7. j2 – 3j – 108. –2x2 + 6x + 56
9. Solve –3u = u2.
23. Find the discriminant of 3p2 – 6p + 8 = 0 and give the number and
type of solutions to the equation.
Lesson
Use Properties of
Exponents
Simplify (5x3y–4)3.
Tell which properties of exponents you used.
Evaluate and Graph
Polynomial Functions
State the degree, type, and leading coefficient of
the polynomial function: g(x) = 6x3 + 9x2 – 7. Then
use direct substitution to evaluate
the polynomial function for x = 3.
Find the sum of 3x2 – 4x + 9 and 4x2 – 5 .
Find the product of the polynomials 3x2 – 4x + 9
and 2x – 5.
Add, Subtract, and
Multiply Polynomials
Factor and Solve
Polynomial Equations
Use your FACTORING Concept Map: You must
know ALL the ways to factor.
Synthetic/Long
Division
Divide 2x2 – 7x + 9 by x – 2 using LONG division
and SYNTHETIC division.
1. Write (4.3 × 104)–2 in scientific notation.
2. Simplify (q2u4)–2.
3. Use direct substitution to evaluate –2x3 + 2x2 + 6x – 4 for
x = –1.
4. Use synthetic substitution to evaluate 2x4 – 4x2 + x – 20 for x = 2.
5. (y5 – 2y2 – y4) + (3y2 – y4)
2
KEY IDEAS/Essential Questions/Formulas/etc.
Exercise
2
6. (x – 2x + 4)(3 – x)
Factor the polynomial completely using any method.
What are ALL the properties of exponents?
7.
1 4
x –4
4
8. y3 + 6y2 – 3y – 18
9. A shipping box is shaped like a rectangular prism. It has a total
volume of 96 cubic inches. The height is two inches less than the
width and the length is eight inches longer than the width. What
are the dimensions of the box?
Divide using polynomial long division or synthetic division.
10. (x3 – 13x – 12) ÷ (x – 4)
11. (x3 + 6x2 – 9x – 54) ÷ (x – 3)
Blast from the Past:
KEY IDEAS/Essential Questions/Formulas/etc.
Exercise
Solving
Equations/Inequalities
Solve & Graph: 8x  6  10
Writing Linear
Equations
Solve & Graph: 16  8r  0
Find the equation of the line that passes through
(2,-3) and (-4, -6).
What is the formula to find the slope of a line between two points?
Find the equation of the line parallel to 2x-8y = 10
that passes through (1,3).
Find the equation of the line perpendicular to
2x-8y = 10 that passes through (-2,5).
Simplifying Radical
Expressions
Simplify:
80 x 3 y 8 z 9
Simplify:
3
Simplify:
What is Slope-Intercept Form?___________________________________
What is Point-Slope Form? ___________________________________
How do you find the equation of a line given two points?
Parallel lines have_______________ slope.
Perpendicular lines have_______________ slope.
What does it mean to rationalize the denominator?
What is a conjugate?
5
3 7
2 6
Parent Functions
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