Module 6: Solving Quadratic Equations

Solving Quadratic Equations

Apply your knowledge of quadratic equations and systems of equations in order to provide your responses. Show complete work where appropriate, and use complete sentences and math vocabulary for your responses.

Part I: Solving Quadratic Equations Algebraically

1. Explain how to determine the solutions to a quadratic equation, algebraically.
2. Create a problem with a quadratic equation that you would solve algebraically and solve it.

Part II: Solving Quadratic Equations Graphically

1. Explain how to determine the solutions to a quadratic equation, graphically.
2. Create a problem with a quadratic equation that you would solve graphically and solve it.

Part III: Create Your Own Quadratic Equation

Create your own quadratic equation, ax2 + bx + c = 0

Step 1: Let a = the numeric month of your birth ÷ 2

• For example, if you were born in May, a = 5 ÷ 2 = 2.5

Step 2: Let b = the date of your birth – 17

• For example, if you were born on the 28th, then b = 28 – 17 = 11

Once you have built your quadratic equation, use the quadratic formula to find the solution set.

Part IV

Lindsey is a member of the swim team at a local university. She has been working hard to perfect her dive for an upcoming swim meet. Lindsey's dive can be modeled by the quadratic equation y = – 16x2 + 33x + 45, where x is time in seconds, and y is Lindsey's height in the air in feet.

1. At what time will Lindsey be 30 feet in the air?
2. How high is the diving board? Explain your thinking.

Reflection

After you have completed the assignment above, take a moment to reflect on the following question. Respond to the question in a brief four to five sentence paragraph.

• Do you prefer to solve quadratic equations by factoring, by using the quadratic formula, or by graphing? Explain.

 

Once you have completed the assignment and reflection, please submit your work to the dropbox.