Download e-book for kindle: Algebra II (Cliffs Quick Review) by Edward Kohn, David Alan Herzog

By Edward Kohn, David Alan Herzog

ISBN-10: 0764563718

ISBN-13: 9780764563713

In terms of pinpointing the belongings you actually need to grasp, not anyone does it larger than CliffsNotes. This speedy, powerful instructional is helping you grasp center algebraic ideas -- from linear equations, relatives and services, and rational expressions to radicals, quadratic platforms, and factoring polynomials -- and get the very best grade.
At CliffsNotes, we're devoted to assisting you do your top, regardless of how hard the topic. Our authors are veteran academics and gifted writers who know the way to chop to the chase -- and nil in at the crucial details you must prevail.

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It is a brief, glossy, and influenced advent to mathematical common sense for higher undergraduate and starting graduate scholars in arithmetic and desktop technology. Any mathematician who's drawn to getting accustomed to common sense and wish to research Gödel’s incompleteness theorems may still locate this e-book quite helpful.

Additional info for Algebra II (Cliffs Quick Review)

Sample text

Y 4 (0,4) 3 2 1 −3 −2 −1 −1 (6,0) 1 2 3 4 5 x 6 2x+3y =12 −2 −3 Notice that Figures 2-6 and 2-7 are exactly the same. Both are the graph of the line 2x + 3y = 12. Example 8: Draw the graph of x = 2. As shown in Figure 2-8, x = 2 is a vertical line whose x-coordinate is always 2. Figure 2-8 x = 2 for all y values. y 3 x=2 2 1 −3 −2 −1 1 2 3 x −1 −2 −3 Example 9: Draw the graph of y = –1. As shown in Figure 2-9, y = –1 is a horizontal line whose y-coordinate is always –1. F 4/19/01 8:50 AM Page 33 Chapter 2: Segments, Lines, and Inequalities Figure 2-9 33 y = –1 for all x values.

If you use the x-intercept and y-intercept method, you get x-intercept (4, 0) and y-intercept (0, 3). If you use the slope-intercept method, the equation, when written in y = mx + b form becomes y= - 34 x + 3 Because the original inequality is <, the boundary line will be a dashed line. Look at Figure 2-11. Figure 2-11 The boundary is dashed. y 4 3 2 1 −3 −2 −1 1 2 3 −1 x 4 3x + 4y = 12 −2 −3 Now, select a point not on the boundary, say (0, 0). Substitute this into the original inequality: 3x + 4y < 12 ?

F 30 4/19/01 8:50 AM Page 30 CliffsQuickReview Algebra II ■ y-intercept. The y-intercept of a graph is the point at which the graph will intersect the y-axis. It will always have an x-coordinate of zero. A vertical line that is not the y-axis will have no y-intercept. One way to graph a linear equation is to find solutions by giving a value to one variable and solving the resulting equation for the other variable. A minimum of two points is necessary to graph a linear equation. Example 6: Draw the graph of 2x + 3y = 12 by finding two random points.