This activity is intended to supplement Algebra I, Chapter 10, Lesson 5.
Time required: 20 minutes
In this activity, students will make connections between the visual ways to find zeros of a parabola and algebraic ways. The quadratic formula is heavily emphasized in this activity, and is utilized in both a calculator program and in the Lists screen.
Topic: Quadratic Formula
Students will see the graph of a parabola, and identify its zeros (x−intercepts).
Students will solve the quadratic by using the quadratic formula, with the discriminant being calculated in a formula in lists.
Students will use a program to solve the quadratic completely.
Teacher Preparation and Notes
The program QUAD has been provided to evaluate the quadratic formula, both the positive and negative solutions. If you would prefer to use this as a teaching opportunity for programming, you can have the students enter the program.
You can also instruct students to enter their own program following your cues.
Students can use the QUAD program to confirm their answers, if obtained using the zero command.
Students will first obtain the solutions for the functions in Question 9 by graphing and finding the zeros or by using the QUAD program.
Finally, lists are used to calculate the value of the discriminant for the previous two problems, whose solutions were irrational.
Now, the lists and formula are available for students to use to calculate the discriminant for other problems provided on the student worksheet as homework, or it can be used to rework any previous problems.
Students will use the formula provided in Question 10 to calculate the discriminant for several other quadratics.
Then, students are to examine the flow chart and discuss with students how to use it to answer their homework problems. Ask students to sketch a different graph for each scenario. One is already shown for them.