New SAT Math Workbook

Note that question 1 is a grid in question in which

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Unformatted text preview: plotting some (x,y) pairs, then connecting the 1 1 points: 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 xy-plane or to identify certain features of the graph of a quadratic equation, or compare two graphs Example: The graph shown in the xy-plane 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. 260 Chapter 15 Example: In the xy-plane, 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 xy-plane 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 real-life situations). 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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