New SAT Math Workbook

# First it is helpful to isolate y in the equation y x2

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Unformatted text preview: e? (A) (B) (C) (D) (E) –2 5 –2 2 5 y= − x–3 9 1 3 2 If h is a linear function, and if h(2) = 3 and h(4) = 1, then h(–101) = (A) –72 (B) –58 (C) 49 (D) 92 (E) 106 3. If two linear function f and g have identical domains and ranges, which of the following, each considered individually, could describe the graphs of f and g in the xy-plane? I. two parallel lines II. two perpendicular lines III. two vertical lines (A) I only (B) I and II only (C) II only (D) II and III only (E) I, II, and III www.petersons.com 258 Chapter 15 8. QUADRATIC FUNCTIONS—EQUATIONS AND GRAPHS In Chapter 8, you learned to solve quadratic equations in the general form ax2 + bx + c = 0 by factoring the expression on the left-hand side of this equation to find the equation’s two roots— the values of x that satisfy the equation. (Remember that the two roots might be the same.) The new SAT may also include questions involving quadratic functions in the general form f(x) = ax2 + bx + c. (Note that a, b, and c are constants and that a is the only essential constant.) In quadratic functions, especially where defining a graph on the xy-plane is involved, the variable y is often used to represent f(x), and x is often used to represent f(y). The graph of a quadratic equation of the basic form y = ax2 or x = ay2 is a parabola, which is a U-shaped curve. The point at which the dependent variable is at its minimum (or maximum) value is the vertex. In each of the following four graphs, the parabola’s vertex lies at the origin (0,0). Notice that the graphs are constructed by tabulating and plotting several (x,y) pairs, and then connecting the points with a smooth curve: 1 The graph of a quadratic equation of the basic form x = y 2 or y = 2 is a hyperbola, which consists of two Ux shaped curves that are symmetrical about a particular line, called the axis of symmetry. The axis of symmetry of 1 the graph of x = y 2 is the x-axis, while the axis of symmetry in the graph of y = 2 is the y-axis, as the next x figure shows. Again, the graphs are constructed by tabulating and...
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## This note was uploaded on 08/15/2010 for the course MATH a4d4 taught by Professor Colon during the Spring '10 term at Embry-Riddle FL/AZ.

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