advertisement

Algebra II with Trigonometry Name Pd. UNIT QF STUDY GUIDE TEST: FRIDAY 11/21 Solve by factoring. 1) 50x2 – 200 = 0 2) 8x2 = 56x 3) 18x3 – 2x2 + 36x = 4 4) 36x2 + 33x - 15 = 0 Solve by finding the square root. 5) x2 – 98 = 0 6) -x2 + 2 = x2 + 14 7) 5x2 – 8 = 4 8) 3 2 x + 6 = 18 4 Solve by completing the square. 9) x2 + 3x – 2 = 0 GD/MPH/RS 1/09 10) 4x2 – 16x = 10 1 Algebra II with Trigonometry Solve using the Quadratic Formula. 11) 6x2 - 19x - 7 = 0 12) 11 = -3x2 – 7x Use the discriminant to determine the nature of the roots for each quadratic equation. Equation Value of the Discriminant Number of Roots Real or Imaginary Roots 13) 6x2 – x + 1 = 0 14) x2 – 2 = -6x 15) -14x2 -12x = 4 16) 9x2 – 12x + 4 = 0 GD/MPH/RS 1/09 2 Algebra II with Trigonometry Graph each quadratic equation. State the vertex, axis of symmetry, x- and yintercepts, and if the graph opens up or down. 17) y = x2 - 2x + 1 18) y = 2x2 + 8x 19) y = -x2 + 6x - 10 20) y > GD/MPH/RS 1/09 1 2 x -4 3 3 Algebra II with Trigonometry Rewrite each equation in vertex form and identify the vertex and axis of symmetry. 21) f(x) = x2 - 8x + 11 22) f(x) = -x2 - 10x 23) f(x) = 2x2 + 24x - 7 24) f(x) = -5x2 + 30x + 2 Solve each of the following word problems. Round to tenths as appropriate. 25) The length of a rectangle is 8 cm less than three times its width. If the area of the rectangle is 476 cm2, find the dimensions of the rectangle. 26) The longer leg of a right triangle is 6 units more than twice the shorter leg. If the hypotenuse is 3 units longer than longer leg, find the dimensions of the right triangle. 27) While standing on the observation deck of the Space Needle (which is 520 feet above the ground), Stanley is debating whether or not to release his ice cream cone on the unsuspecting crowd below. How long will it take the ice cream cone to hit the ground if: a) he drops the cone? GD/MPH/RS 1/09 b) he throws the cone up at 40 ft/s? 4 Algebra II with Trigonometry ANSWERS (Match answers to Questions #1 - 12) A. ±4 B. C. ±7 2 D. E. 0, 7 F. G. -2, 2 H. I. 2± K. 26 2 2 15 ± 5 3 ± 17 2 1 , ± 2i 9 -1 7 , 3 2 ± 6i J. L. Question 13 14 15 16 Value of the Discriminant -23 44 -80 0 -5 1 , 4 3 -7 ± 83i 6 Number of Roots 2 2 2 1 Real or Imaginary Roots imaginary real imaginary real GRAPHS Question Vertex 17 18 19 20 (1, 0) (-2, -8) (3, -1) (0, -4) 21) 22) 23) 24) f(x) f(x) f(x) f(x) = (x-4)2 – 5 = -(x+5)2 + 25 = 2(x+6)2 – 79 = -5(x-3)2 + 42 25) 14 cm by 34 cm 27A) 5.7 seconds GD/MPH/RS 1/09 Axis of Symmetry x=1 x = -2 x=3 x=0 x-intercept(s) y-intercept (1, 0) (0, 0), (-4, 0) none ( 2 3 , 0) (0, 1) (0, 0) (0, -10) (0, -4) vertex (4, -5) vertex (-5, 25) vertex (-6, 79) vertex (3, 42) Opens Up or Down up up down up AOS x = 4 AOS x = -5 AOS x = -6 AOS x =3 26) 15, 36, 39 27B) 7.9 seconds 5