Definition/Procedure Example Graph x Vertex: (2, 4) Axis of symmetry: y 4 a opens to the right. The domain is 2, q); the range is (q, q). Chapter 10: Review Exercises (10.1) Solve using the square root property. 1) d 2 144 2) m2 75 3) v2 4 0 4) 2c2 11 25 5) (b 3)2 49 6) (6y 7)2 15 0 1 2 ( y 4)2 2. 1 2 , so the graph 1 t t t 7) 27k2 30 0 8) (j 14)2 5 0 9) Find the distance between the points (8, 3) and (12, 5). 10) A rectangle has a length of 512 in. and a width of 4 in. How long is its diagonal? The graph of the quadratic equation x ay2 by c is a parabola that opens in the x-direction, or horizontally. The quadratic equation x ay2 by c can also be written in the form x a(y k)2 h. When it is written in this form we can fi nd the following. 1) The vertex of the parabola is (h, k). 2) The axis of symmetry is the horizontal line y k. 3) If a is positive, the graph opens to the right. If a is negative, the graph opens to the left. (p. 672) 10.7 Quadratic and Rational Inequalities A quadratic inequality can be written in the form ax2 bx c 0 or ax2 bx c 0 where a, b, and c are real numbers and a 0. ( and may be substituted for and .) (p. 681) An inequality containing a rational expression, like c 5 c 1 0, is called a rational inequality. (p. 685) Solve r 2 4r 12. Step 1: r 2 4r 12 0 Subtract 12. Because the inequality symbol is , the solution set contains the interval(s) where the quantity r2 4r 12 is positive. Step 2: Solve r 2 4r 12 0. (r 6)(r 2) 0 Factor. r 6 0 or r 2 0 r 6 or r 2 Step 3: Put r 6 and r 2 on a number line. 2 r2 r 12 Step 4: Choose a test number in each interval to determine the sign of r 2 4r 12. Step 5: The solution set will contain the numbers in the intervals where r 2 4r 12 is positive. Step 6: The endpoints of the intervals are included because the inequality is . The graph of the solution set is 5 2 1 1 2 5 1 The solution set of r 2 4r 12 is (q, 2 ´ 6, q). x y V 2 x y 2 2 1 2 696 CHAPTER 10 Quadratic Equations and Functions www.mhhe.com/messersmith
messersmith_power_intermediate_algebra_1e_ch4_7_10
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