**Title:** Family Ties: Parabolas

**Description:**
This lesson allows students to manipulate the parameters while using the vertex form of the equation of a parabola to see the effects on the graph. The spreadsheet can be altered for other functions.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMS-U Project.

**Standard(s): **

[TC2] CA2 (9-12) 5: Utilize advanced features of spreadsheet software, including creating charts and graphs,
sorting and filtering data, creating formulas, and applying functions.

[MA2013] AL1 (9-12) 28: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. *Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.** [F-IF4]

[MA2013] AL1 (9-12) 18: Solve quadratic equations in one variable. [A-REI4]

[MA2013] AL1 (9-12) 21: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. [A-REI7]

[MA2013] AL1 (9-12) 31: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [F-IF7]

[MA2013] AL1 (9-12) 33: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [F-IF9]

[MA2013] AL1 (9-12) 36: Identify the effect on the graph of replacing *f*(*x*) by *f*(*x*) + *k*, *k* *f*(*x*), *f*(*kx*), and *f*(*x* + *k*) for specific values of *k* (both positive and negative); find the value of *k* given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. [F-BF3]

[MA2013] AL2 (9-12) 6: (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. [N-CN9]

[MA2013] AL2 (9-12) 32: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [F-IF9]

[MA2013] ALC (9-12) 6: Use the extreme value of a given quadratic function to solve applied problems. (Alabama)

[MA2013] ALT (9-12) 4: Solve quadratic equations with real coefficients that have complex solutions. [N-CN7]

[MA2013] ALT (9-12) 6: (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. [N-CN9]

[MA2013] ALT (9-12) 32: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [F-IF9]

[MA2013] AM1 (9-12) 11: (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. Understand the importance of using complex numbers in graphing functions on the Cartesian or complex plane. [N-CN9] (Alabama)