College Algebra Solve and Graph Quadratic Equations

Use this template to insert your answers for the assignment.  Please use one of the four methods for showing your work (EE, Math Type, ALT keys, or neatly typed). Work should be clear and legible.

Problems need to include all required steps and answer(s) for full credit.  All answers need to be reduced to lowest terms where possible.

Solve the following polynomials for the given variable.

1.  (2x-1) (x+3) = 0

2.  121 = y2

3.  2×2 – x = 3

4.  -12 = x2 – 13x

5.  6×2 – 10x – 4 = 0

6.  x2 – 9x +5 = 0

7.  x2 – 8x -16 = 0

8.  3×2 + 5x = 8

9.  -2×2 – 3 = 3x

10.  -x2 + 2x – 4 = 0

Graph the following equations on a coordinate plane.

Go to ‘insert’ and ‘shapes’, and use the line feature to graph.

12.  –x2 – 3x – 2 = 0

13.  x2 – 4 = 0

14.  x2 + 6x + 8 = 0

15.  x2 + 7x = -10

1.  When do you use the quadratic formula to solve for a quadratic equation?  Explain.

2.  A water balloon is thrown off a three-story building at a height of 30 ft. with a velocity of 18 feet per second.  Using the given equation, find the time it takes for the ball to reach 6 feet from the ground.

3.  The demand for a brand of coffee makers is represented by the equation

-c2 + 200c = 0

Solve the equation to find the maximum demand for the coffee makers.

4.  A toy rocket takes off with an initial velocity of 14 feet per second.  If t represents the time after the rocket takes off, find the time it takes for the rocket to reach 214 feet.

h = 16t2 +14t + 0

5.  A triangular sand box has one leg that is 2 feet shorter than the other leg.  If the hypotenuse is 5 feet longer than the shorter leg, find the approximated length of each side of the right triangle.  Round each side to the nearest tenth.  (Hint:  Use the Pythagorean Theorem a2 + b2 = c2.)

6.  A rectangular pool has a length that is 9 feet more than its width.  If the area of the pool is 162 square feet, find the width and length.

What are the methods for solving a quadratic equation? Discuss each one.

Explain which points are needed to graph a quadratic equation and how to find them.

Create your own quadratic equation and explain the graph of it.  Discuss how you found the points for the graph.

College Algebra Solve and Graph Quadratic Equations

Use this template to insert your answers for the assignment.  Please use one of the four methods for showing your work (EE, Math Type, ALT keys, or neatly typed). Work should be clear and legible.

Problems need to include all required steps and answer(s) for full credit.  All answers need to be reduced to lowest terms where possible.

Solve the following polynomials for the given variable.

1.  (2x-1) (x+3) = 0

2.  121 = y2

3.  2×2 – x = 3

4.  -12 = x2 – 13x

5.  6×2 – 10x – 4 = 0

6.  x2 – 9x +5 = 0

7.  x2 – 8x -16 = 0

8.  3×2 + 5x = 8

9.  -2×2 – 3 = 3x

10.  -x2 + 2x – 4 = 0

Graph the following equations on a coordinate plane.

Go to ‘insert’ and ‘shapes’, and use the line feature to graph.

12.  –x2 – 3x – 2 = 0

13.  x2 – 4 = 0

14.  x2 + 6x + 8 = 0

15.  x2 + 7x = -10

1.  When do you use the quadratic formula to solve for a quadratic equation?  Explain.

2.  A water balloon is thrown off a three-story building at a height of 30 ft. with a velocity of 18 feet per second.  Using the given equation, find the time it takes for the ball to reach 6 feet from the ground.

3.  The demand for a brand of coffee makers is represented by the equation

-c2 + 200c = 0

Solve the equation to find the maximum demand for the coffee makers.

4.  A toy rocket takes off with an initial velocity of 14 feet per second.  If t represents the time after the rocket takes off, find the time it takes for the rocket to reach 214 feet.

h = 16t2 +14t + 0

5.  A triangular sand box has one leg that is 2 feet shorter than the other leg.  If the hypotenuse is 5 feet longer than the shorter leg, find the approximated length of each side of the right triangle.  Round each side to the nearest tenth.  (Hint:  Use the Pythagorean Theorem a2 + b2 = c2.)

6.  A rectangular pool has a length that is 9 feet more than its width.  If the area of the pool is 162 square feet, find the width and length.

What are the methods for solving a quadratic equation? Discuss each one.

Explain which points are needed to graph a quadratic equation and how to find them.

Create your own quadratic equation and explain the graph of it.  Discuss how you found the points for the graph.

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