Download Algebra 2 Unit 2 Notebook Guide

Name:________________________
Algebra 2
Unit 2
Notebook Guide
Unit Topic: Quadratic Functions and Factoring—Part 2 (Chapter 4)
Date
Lesson
Textbook Section Homework Assignment
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1. Perform Operations with Complex Numbers
4.6 HW #1 (p. 279) 3, 7, 13, 17, 25, 33, 35, 43, [53, 59]
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2. Complete the Square
4.7 HW #2 (p. 288) 3, 7, 13, 19, 23, 27, 45, 47, [55, 60]
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3. Use the Quadratic Formula and the Discriminant
4.8 HW #3 (p. 296) 3, 5, 7, 19, 23, 27, 31, 39, [45, 63]
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4. Quadratic Problem Solving
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5. Graph and Solve Quadratic Inequalities
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6. Write Quadratic Functions and Models
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7. Unit 2 Review
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8. Problem Solving
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9. Unit 2 Test
HW #4 (Handout) 1, 2, 3, 4, 5, 6, 7, 8
4.9 HW #5 (p. 304) 7, 9, 11, 17, 21, 25, 47, 49, [69]
4.10 HW #6 (p. 312) 3, 9, 11, 17, 21, 25, 31, 37, [41, 45]
Unit 2 Review
4.6-4.10 Problem Solving (p. 316) 1, 2, 3, 8
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Note: Please label your homework assignment as shown above along with your name.
Grade Tracking
Homework Quiz #1
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Homework Quiz #2
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Homework Quiz #3
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Problem Solving
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Unit 2 Test
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Unit 2 Points Earned
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Unit 2 Possible Points
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Unit 2 Average
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Unit 2 Grade
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Cumulative Average
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Cumulative Grade
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Algebra 2 Concepts - Unit 2 (textbook sections 4.6 – 4.10)
A complex number is of the form a + bi, in which the a term is a real number and the bi term is an
imaginary number. By definition, i equals the square root of negative one, a non-real value.
Complex numbers extend the idea of the one-dimensional number line to the two-dimensional
complex plane by using the number line for the real part and the vertical axis to plot the imaginary
part. In this way the complex numbers include the ordinary real numbers while extending them in
order to solve problems that would be impossible with only real numbers.
A perfect square trinomial is what results from squaring a binomial. Start with a binomial, for
example x + 5. Square it and you will have a perfect square trinomial, in this case (x + 5)2 or
equivalently (x + 5)( x + 5) produces the perfect square trinomial x2 + 10x + 25. Completing the
square is a process in which a perfect square trinomial is created and then factored in order to
rewrite or solve a quadratic equation. In fact, the quadratic formula, the general solution to all
quadratic equations, can be derived using this process.
The discriminant of a quadratic equation written in the standard form ax2 + bx + c = 0 is the
expression b2 − 4ac. You find this expression in the quadratic formula under the square root sign.
The discriminant determines the number and type of solutions. A quadratic equation with real
coefficients can have either one or two real solutions, or two imaginary solutions. If the
discriminant is positive, then there are two distinct real roots. If the discriminant is zero, then there
is one distinct real root. If the discriminant is negative, then there are two distinct complex roots.
A best-fitting regression model is a mathematical equation used to approximate the relationship
between variables observed in the real world. Depending on the data, the model may be a linear
function, a quadratic function, or from some other family of functions. How close the equation
comes to matching the data is referred to as the “goodness-of-fit”, and the chosen function is
typically the one that fits the best, as measured by the correlation coefficient.