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Unformatted text preview: plotting some (x,y) pairs, then connecting the 1 1 points: www.petersons.com Numbers and Operations, Algebra, and Functions 259 The new SAT might include a variety of question types involving quadratic functions—for example, questions that ask you to recognize a quadratic equation that defines a particular graph in the xyplane or to identify certain features of the graph of a quadratic equation, or compare two graphs Example: The graph shown in the xyplane above could represent which of the following equations? (A)  x2  =  y2  (B) x = y2 (C)  y  = x2 (D) y = x2 (E)  x  = y2 Solution: The correct answer is (C). The equation  y  = x2 represents the union of the two equations y = x2 and –y = x2. The graph of y = x2 is the parabola extending upward from the origin (0,0) in the figure, while the graph of –y = x2 is the parabola extending downward from the origin. www.petersons.com 260 Chapter 15 Example: In the xyplane, the graph of y + 2 = shows a parabola that opens 2 (A) downward. (B) upward. (C) to the right. (D) to the left. (E) either upward or downward. Solution: The correct answer is (B). Plotting three or more points of the graph on the xyplane should show the parabola’s orientation. First, it is helpful to isolate y in the equation y =
x2 − 2 . In this equation, 2 x2 substitute some simple values for x and solve for y in each case. For example, substituting 0, 2, and –2 for x gives us the three (x,y) pairs (0,–2), (2,0), and (–2,0). Plotting these three points on the xyplane, then connecting them with a curved line, suffices to show a parabola that opens upward. An SAT question might also ask you to identify a quadratic equation that defines two or more domain members and the corresponding members of the function’s range (these questions sometimes involve “models” of reallife situations). www.petersons.com Numbers and Operations, Algebra, and Functions 261 Exercise 8
Work out each problem. Circle the letter that appears before your answer. 1. Which of t...
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