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?
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 x2 + bx + c = 0 by
Factoring
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
Use the Quadratic Formula
and the Discriminant
Write the expression as a complex number in
standard form.
(2 – 5i)(–3 + 9i)
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
Find the zeros of the function by rewriting in intercept form.
9. f(x) = 2x2 – 4x
10. y = 2x2 – 11x – 21
11. Simplify 6• 12 • 6 • 2.
Graph the function. Label the vertex and the axis of symmetry.
For Exercise 5, also label the x–intercepts.
3. y =
1
(x + 1)2 – 2
2
Solve the equation.
12. 25x2 = 16
13. x2 – 3x + 5 = 0
4. y = –2(x – 1)(x – 2)
14. Write
1  3i
as a complex number in standard form.
2  5i
15. Write (3 – 2i) – (–11 – 9i) as a complex number in standard form.
5. Tell whether y = –3(x + 1)2 + 4 has a minimum value or a
maximum value. Then find that value.
Factor the expression.
6. j2 – 3j – 10 7. –2x2 + 6x + 56
8. Solve –3u = u2.
16. Solve r2 = 18 – 7r.
17. Find the discriminant of 3p2 – 6p + 8 = 0 and give the number and
type of solutions to the equation.
Chapter 2:
Lesson
Exercise
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
KEY IDEAS/Essential Questions/Formulas/etc.
What are ALL the properties of exponents?
Factor and Solve
Polynomial Equations
You must know ALL the ways to factor.
Synthetic/Long
Division
Divide 2x2 – 7x + 9 by x – 2 using LONG division
and SYNTHETIC division.
Simplifying Radical
Expressions
Simplify:
80 x 3 y 8 z 9
What does it mean to rationalize the denominator?
Simplify:
3
What is a conjugate?
Simplify:
Finding Factors and
Solutions of
Polynomials Using the
Factor Theorem and
Rational Zero Test
5
3 7
2 6
Find all of the real zeros of the polynomial
How do factors and solutions relate?
2x – 4x + x – 20
4
2
What is the rational zero test?
1. Simplify (q2u4)–2.
Factor the polynomial completely using any method.
6.
1 4
x –4
4
7. y3 + 6y2 – 3y – 18
2. Use direct substitution to evaluate –2x3 + 2x2 + 6x – 4 for
x = –1.
Divide using polynomial long division or synthetic division.
8. (x3 – 13x – 12) ÷ (x – 4)
3. Use synthetic substitution to evaluate 2x4 – 4x2 + x – 20 for x = 2.
9. (x3 + 6x2 – 9x – 54) ÷ (x – 3)
4. (y5 – 2y2 – y4) + (3y2 – y4)
5. (x2 – 2x + 4)(3 – x)2