Challenge Problem: Analyzing Quadratic Functions

Analyzing Quadratics - Due 3/17/14

We have spent three weeks talking about functions. You have previously learned about quadratic functions, how to graph them, how to factor them, and how to solve them.

PROJECT:

1.    Choose 6 quadratic equations of the following:

§   Two equations with rational roots

§   Two equations with irrational roots

§   Two equations with complex roots.

2.     You will graph quadratics in standard form(y = ax² + bx + c). You must identify precisely how to find the x – intercepts, y – intercept, equation of the axis of symmetry, coordinate of the vertex and complete the graph.

3.     You will solve each equation using the Quadratic Formula.

            

4.   Use your observations to summarize the following. (No less than a page)

§   Explain how to use the quadratic formula to solve quadratic equations.

§   What are some advantages and disadvantages of the quadratic formula?

§   According to your table below, how do the roots relate to the graphs of the functions?

§   What do you notice the number of roots and the value of the radicand in Function #1 and in Function #3?

§   How does the value of the radicand tell you about the roots of the quadratic functions?

5.     Complete the following table according to your graphs and solutions

FUNCTIONS	SOLUTIONS	TYPES OF THE SOLUTION	VALUE OF THE RADICAND	# OF X – INTERCEPTS BY GRAPHING
1)		RATIONAL NUMBERS
2)		RATIONAL NUMBERS
3)		IRRATIONAL NUMBERS
4)		IRRATIONAL NUMBERS
5)		COMPLEX NUMBERS
6)		COMPLEX NUMBERS

6.  Make sure you staple rubric page, table page, and written summary to your project. There will be 10 points deducted for each day your project is late.

RUBRIC

  

REQUIREMENTS	COMMENTS	YOUR POINTS	POINTS POSSIBLE
GRAPHING USING THE FIVE STEP METHOD § FINDS X – INTERCEPTS: 2 POINTS X 6 § FINDS Y – INTERCEPT:   1 POINT X 6 § FINDS EQUATIONS OF THE AXIS OF SYMMETRY: 1 POINT X 6 § FINDS COORDINATE OF VERTEX: 1 POINT X 6			30
SOLVING EQUATIONS BY USING THE QUADRATIC FORMULA: 5 POINTS X 6			30
SUMMARY OF THE TABLE: 10 POINTS			10
WRITTEN SUMMARY : 20 POINTS			20
WORK IS NEATLY MOUNTED ON A SHEET OF PAPER AS THE FOLLOWING ORDER: §  COVER – PAGE §  RUBRIC – PAGE §  YOUR WORK §  SUMMARY TABLE §  WRITTEN SUMMARY			10
DATE TURN IN			100
TOTAL POINTS EARNED