Review the following concepts if needed:
 Solving by Factoring and Square Root Methods for Intermediate Algebra
 Completing the Square and the Quadratic Formula for Intermediate Algebra
 Graphs of SecondDegree Equations for Intermediate Algebra
 Quadratic and Rational Inequalities for Intermediate Algebra
Problems
6.1
Use the factor method to solve the following. Check for extraneous roots where applicable.
 y^{2} – 8y + 15 = 0
 t^{2} – 3t = 10
 2s^{2} – 7s + 5 = 0
 2p^{2} – 5p = p
 (x + 10) (2x – 7) = 0
6.2
Use the factor method to solve the following. Check for extraneous roots where applicable.
 r^{2} = 10
 3y^{2} + 1 = 28
 2x^{2} + 26 = 0
 (2s + 1)^{2} = 7
 (3w – 4)^{2} + 8 = 0
6.3
Determine the term that would complete the square for each of the following.
 x^{2} + 18x
 y^{2} – 9y
6.4
Solve by completing the square.
 x^{2} – 4x – 11 = 0
 y^{2} + 6y = –2
 3t^{2} – 6t – 2 = 0
 4p^{2} + 7p + 2 = 3
6.5
Use the quadratic formula to solve the following.
 x^{2} + 5x – 10 = 0
 t^{2} – 17 = 2t
 2y^{2} + 2 = 2y + 7
6.6
Use a calculator and the quadratic formula to solve the following.
 5.21x^{2} + 1.17x – 0.98 = 0
 2.38x^{2} – 4.77x + 3.05 = 0
6.7
Solve the following. Remember to check for extraneous solutions.
6.8
Solve.
6.9
Solve.
 y^{6} – 8y3 + 12 = 0
 x^{4} – 7x^{2} – 18 = 0
 12w^{4} + 5w^{2} – 2 = 0
 2x–^{2} – 3x–^{1} – 20 = 0
6.10
Solve. State the answer in complete sentence form. Employ a calculator when necessary.
 The height in feet of a ball thrown vertically upward is given by h = 48t – 16t^{2}, where t is the time in seconds after the throw. How long will it take the ball to reach a height of 32 ft?
 Find the radius of a circular region with area 6,940 ft^{2}.
 Find the radius of a cylindrical container 8 meters high that contains 1,608 m^{3} of material.
 A diagonal brace is necessary on a gate that is 3 feet by 5 feet. How long must the brace be if it is attached at the corners of the gate?
 A square with a diagonal of length 17 feet is to be constructed. How long must the sides of the square be?
 The cost C in dollars of producing n gadgets is given by C = 1,200 + 12n – 6n^{2}. How many gadgets can be produced at a cost of $192?
 Find the dimensions of a rectangle with area 4,500 cm2 if the width is 80% of the length.
 A jet requires 7 hr 10 min to complete a round trip of 1,785 miles each way. The plane had a 70 mph headwind going and a 60 mph tailwind on the return trip. Find how fast the jet travels in still air.
6.11
Graph the following.
 y = x^{2} – 4
 y = x^{2} – 6x + 7
 y = –x^{2} – 4x + 5
 x = y^{2} +1
 x = y^{2} – y – 12
 x = –y^{2} – 4y –5
6.12
Graph the following on a graphing calculator. Employ the trace feature to approximate the zeros (roots) and vertex of each. Express answers to three decimal place accuracy.
 y = x^{2} – 3.6x – 1.1
 y= –0.8x^{2} – 6.6x – 10.7
 y= –1.1x^{2} – 5.5x – 7.9 .
6.13
Solve the following. (Use a sign diagram to help in identifying the solution in each case.) Express the solution set in interval notation.
 x – 3x – 4 < 0
 2x^{2} – x – 15 ≥ 0
 4x^{2} + 4x ≤ 35

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