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Second-Degree Equations and Inequalities Supplementary Problems for Intermediate Algebra

By — McGraw-Hill Professional
Updated on Aug 12, 2011

Review the following concepts if needed:

Problems

6.1

Use the factor method to solve the following. Check for extraneous roots where applicable.

  1. y2 – 8y + 15 = 0
  2. t2 – 3t = 10
  3. 2s2 – 7s + 5 = 0
  4. 2p2 – 5p = p
  5. (x + 10) (2x – 7) = 0

6.2

Use the factor method to solve the following. Check for extraneous roots where applicable.

  1. r2 = 10
  2. 3y2 + 1 = 28
  3. 2x2 + 26 = 0
  4. (2s + 1)2 = 7
  5. (3w – 4)2 + 8 = 0

6.3

Determine the term that would complete the square for each of the following.

  1. x2 + 18x
  2. y2 – 9y

6.4

Solve by completing the square.

  1. x2 – 4x – 11 = 0
  2. y2 + 6y = –2
  3. 3t2 – 6t – 2 = 0
  4. 4p2 + 7p + 2 = 3

6.5

Use the quadratic formula to solve the following.

  1. x2 + 5x – 10 = 0
  2. t2 – 17 = 2t
  3. 2y2 + 2 = 2y + 7

6.6

Use a calculator and the quadratic formula to solve the following.

  1. 5.21x2 + 1.17x – 0.98 = 0
  2. 2.38x2 – 4.77x + 3.05 = 0

6.7

Solve the following. Remember to check for extraneous solutions.

6.8

Solve.

6.9

Solve.

  1. y6 – 8y3 + 12 = 0
  2. x4 – 7x2 – 18 = 0
  3. 12w4 + 5w2 – 2 = 0
  4. 2x2 – 3x1 – 20 = 0

6.10

Solve. State the answer in complete sentence form. Employ a calculator when necessary.

  1. The height in feet of a ball thrown vertically upward is given by h = 48t – 16t2, where t is the time in seconds after the throw. How long will it take the ball to reach a height of 32 ft?
  2. Find the radius of a circular region with area 6,940 ft2.
  3. Find the radius of a cylindrical container 8 meters high that contains 1,608 m3 of material.
  4. 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?
  5. A square with a diagonal of length 17 feet is to be constructed. How long must the sides of the square be?
  6. The cost C in dollars of producing n gadgets is given by C = 1,200 + 12n – 6n2. How many gadgets can be produced at a cost of $192?
  7. Find the dimensions of a rectangle with area 4,500 cm2 if the width is 80% of the length.
  8. 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.

  1. y = x2 – 4
  2. y = x2 – 6x + 7
  3. y = –x2 – 4x + 5
  4. x = y2 +1
  5. x = y2y – 12
  6. x = –y2 – 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.

  1. y = x2 – 3.6x – 1.1
  2. y= –0.8x2 – 6.6x – 10.7
  3. y= –1.1x2 – 5.5x – 7.9
  4. .

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.

  1. x – 3x – 4 < 0
  2. 2x2x – 15 ≥ 0
  3. 4x2 + 4x ≤ 35
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