10.4 Exercises Do the exercises, and check your work. Objective 1: Graph Basic Parabolas 1) What is the vertex of a parabola? 2) What is the axis of symmetry of a parabola? Graph. 3) y x2 1 4) y x2 2 5) y x2 6) y (x 2)2 7) y (x 1)2 8) y (x 1)2 9) y x2 5 10) y x2 4 11) y (x 3)2 12) y 1 2 x2 Objective 2: Graph a Quadratic Equation of the Form y ax2 bx c 13) Explain how to fi nd the vertex of a parabola with equation y ax2 bx c. 14) How do you know whether the graph of y ax2 bx c opens upward or downward? If a 0, the parabola opens upward. If a 0, the parabola opens downward. Sketch the graph of each equation. Identify the vertex. 15) y x2 4 (0, 4) 16) y x2 1 (0, 1) 17) y x2 1 (0, 1) 18) y x2 5 (0, 5) 19) y (x 3)2 (3, 0) 20) y (x 2)2 (2, 0) 21) y x2 4x 3 (2, 1) 22) y x2 6x 5 23) y x2 2x 3 24) y x2 2x 8 25) y x2 2x 4 26) y x2 4x 1 27) y x2 6x 11 28) y x2 8x 17 29) y x2 2x 1 30) y x2 6x 9 31) y 2x2 4x (1, 2) 32) y 2x2 8x 6 (3, 4) (1, 4) (1, 9) (1, 5) (2, 3) (3, 2) (4, 1) (1, 0) (3, 0) (2, 2) The solutions of ax2 bx c 0 are the x-intercepts of the corresponding quadratic equation y ax2 bx c. Use a graphing calculator to solve each equation in Exercises 33–38 by fi nding the x-intercepts of the graph of the corresponding equation, y ax2 bx c. Round your answer to the nearest hundredth where appropriate. 33) 5x2 17x 6 0 34) 4x2 5x 6 0 35) 8x2 38x 9 0 36) 20x2 64x 35 0 37) x2 2x 6 0 38) x2 10x 22 0 *Additional answers can be found in the Answers to Exercises appendix. It is the lowest point of a graph that opens upward or the highest point of a graph that opens downward. It is the line that cuts the parabola in half so that one half of the parabola is the mirror image of the other half. {0.4, 3} {4.5, 0.25} {3.65, 1.65} {0.75, 2} {0.7, 2.5} {6.73, 3.27} R2) Are there any problems you could not do? If so, write them down or circle them and ask your instructor. R1) What do you think the equation of a parabola that opens to the left would be? What about one that opens to the right? 638 CHAPTER 10 Quadratic Equations www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
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