MA101 TEST 3 REVIEW PACKET
Chapters 5, 7 and 8
Square Root Property --Sections 8.1 and 7.7
1.
In your own words, define quadratic equation.
2.
What is the Square Root Property? Explain how to use the Square
Root Property to solve the equation (x-3)2 = 25.
3.
What is the imaginary unit? Express the following in terms of i and
simplify: (a) 25 , and (b) 18
4.
What is a complex number? Give an example.
5.
Do problems 1-5 and 11-13 on Page 632. Check your answers
against the answers in the back of the book on Page A42.
6.
In your own words, define compound interest and describe the
compound interest formula: A = P(1 + r)t.
7.
Review the HW problems from your textbook.
Zero-Product Principle – Sections 5.2 – 5.7 (omit Section 5.6)
1.
Explain in your own words how to multiply monomials. Give an
example.
2.
Explain how to multiply a binomial and a trinomial. Give an example.
3.
What is the FOIL method and when is it used? Give an example.
4.
Do problems 9-12 on the Chapter Test, Page 382 and check your
answers on Page A26.
5.
What is the GCF of a polynomial? Explain how to factor the GCF out
of a polynomial. Give an example.
6.
Review the strategy for factoring polynomials on Page 356. Do
problems 18, 22, 23 and 24 on the Chapter Test, Page 383 and check
your answers on Page A26.
7.
What is the Zero-Product Principle? List the steps for solving a
quadratic equation by using the Zero-Product Principle. Why do you
need to know how to factor to use the Zero-Product Principle? Do
problems 34, 35 and 36 on the Chapter Test, Page 383 and check
your answers on Page A26.
8.
Review the HW problems from your textbook.
Quadratic Formula --Section 8.2
1.
What is the Quadratic Formula? List the steps for using the Quadratic
Formula to solve a quadratic equation. Use the Quadratic Formula to
solve the following equation: 2x2 = -4x + 5.
2.
What is the discriminant? Explain how to use the discriminant to
determine the number and kind of solutions to a quadratic equation. If
a discriminant equals 64, how many and what kind of solutions will the
equation have? What if the discriminant equals -50? What if the
discriminant equals 0?
3.
4.
You have learned three methods for solving a quadratic equation.
Describe in your own words:
(a) when you would choose to use the Square Root Property,
(b) when you would choose to use the Zero-Product Principle, and
(c) when you would choose to use the Quadratic Formula.
Give an example for each case.
Review the HW problems from MathXL and your textbook.
Graphs and Modeling – Section 8.3 and Supplement
1. Consider the quadratic function f(x) = ax2 + bx + c.
--What is the graph of the function shaped like and what is the name of
the shape?
--Describe how you can tell if the graph opens upward or downward.
--What point on the graph is called the vertex? List the steps used to
determine the coordinates of the vertex.
--Describe what the axis of symmetry is. How do you determine the
equation of the axis of symmetry?
--What point or points on the graph is a y-intercept? How many yintercepts are possible? Explain how to find the y-intercept(s).
--What point or points on the graph is an x-intercept? How many xintercepts are possible? Explain how to find the x-intercept(s).
--Graph the function f(x) = -2x2 – 2x + 4, by (a) determining if the
graph opens upward or downward, (b) finding the vertex, (c) finding the
y-intercept(s), (d) finding the x-intercept(s), and (e) using these points
to draw the graph. Sketch in the axis of symmetry and state its
equation. Use the graph to determine the domain and range of the
function.
2. Explain in your own words how the solutions to a quadratic equation
correspond to the x-intercepts of the corresponding quadratic function.
Explain how to use the Square Root Property, the Zero-Product Property
or the Quadratic Formula to find the x-intercepts of a quadratic function. If
using the Quadratic Formula, explain how the discriminant will tell you how
many times the graph crosses the x-axis.
3. Do problems 15, 17 and 19 on the Chapter Test, Page 634-5 and check
your answers on Page A43.
4. When a situation is modeled by a quadratic function, explain how to find
the minimum or maximum values for the function. Do problem 18 on the
Chapter Test, Page 634 and problem 20 on Page 635 and check your
answers on Page A43.
5. Given data presented in tables or graphs, use your calculator to find a
quadratic model of the data. Use the model to make predictions. If
appropriate, interpret the vertex, x-intercepts and y-intercept in the context
of the problem.