### Chapter 9 - Algebra Coach Exercises

**Algebra Coach Exercise on the completing-the-square method.**

Complete the square in each of the following quadratic expressions.
To do this drag-and-drop each of the expressions into the
Algebra Coach and click the Complete the Square button.
- x^2 + 6 x + 4
- x^2 - 4 x + 1
- x^2 + 8 x + 10
- 3 x^2 + 12 x + 3
- x^2 + 8 x + 23
- 3 x^2 + 12 x + 15
- 12 x^2 + 12 x + 7
- 4 x^2 + 4 x + 9

**Algebra Coach Exercise on
factoring by completing the square.**

Factor each of the following quadratic expressions. To do this
drag-and-drop each of these problems into the
Algebra Coach and click the Factor button.
- x^2 + 6 x + 4
- x^2 - 4 x + 1
- x^2 + 8 x + 10
- 3 x^2 + 12 x + 3
- 12 x^2 + 12 x - 1
- 4 x^2 + 4 x - 1

**Algebra Coach Exercise on
factoring by completing the square (the complex case).**

Factor each of the following expressions. To do this
drag-and-drop each of these problems into the
Algebra Coach and click the Factor button.

Required Options settings: the complex number option must be turned on.
- x^2 + 6 x + 11
- x^2 - 4 x + 7
- x^2 + 8 x + 23
- 3 x^2 + 12 x + 15
- 12 x^2 + 12 x + 7
- 4 x^2 + 4 x + 9

**Algebra Coach Exercise on quadratic equations.**

Solve each of the following quadratic equations.
To do this drag-and-drop each of them into the
Algebra Coach and click the AutoSolve button. They can be solved by graphing, factoring,
completing the square or quadratic formula. You can select the method used by clicking
on the “solve quadratics by” panel of the status panel at the bottom of the program.

The quadratics in questions 1 to 5 are incomplete (i.e. either *b* = 0 or *c* = 0)
so they can be solved by more basic methods than the
rest of the equations.
- 2x = 5x^2
- 3x(x - 2) = x(x + 3)
- 5x^2 - 3 = 2x^2 + 24
- (x + 2)^2 = 4x + 5
- 8.25 x^2 - 2.93 x = 0

Solve these quadratic equations by completing the square.
- x^2 + 2 x - 15 = 0
- x^2 - x - 20 = 0
- x^2 - x - 2 = 0
- x^2 + 3 x + 2 = 0
- x^2 - 7 x - 18 = 0

Solve these quadratic equations by factoring.
- x^2 + 12 x + 32 = 0
- x^2 - 12 x - 64 = 0
- 2 x^2 - 3 x - 5 = 0
- 2 x^2 + 5 x - 12 = 0
- 5 x^2 + 14 x - 3 = 0

Solve these quadratic equations by using the quadratic formula.
- 2 + x - x^2 = 0
- - 26 x + 5 - 24 x^2 = 0
- 2 x^3 + x^2 - 18 = x(2 x^2 + 3)
- (2 - x)/3 = 2 x^2
- x(x - 5) = 36

Solve these quadratic equations by graphing.
- 4x^2 - 3x - 5 = 0
- 3x^2 + 6x - 4 = 0
- 4x^2 + 7x - 5 = 0
- x^2 - 12x + 28 = 0
- x^2 - 6x + 7 = 0