Graphs+of+Quadratics

Graphing Quadratics F.IF.7: Graph quadratic functions.
 * __Goals__**

a. Graph by hand using appropriate tools (graph paper, hand drawn coordinate grid)

b. Graph using a graphing calculator

c. Identify/interpret key features of the graphs

d. Identify the domain and range (review).

__**Learning Cycle**__: Level: Procedures with Connections: Deeper levels of understanding and some degree of cognitive effort to connect the similarities and differences of the various functions. Anticipation: x,y coordinates (and axes) order will get mixed up. Algebraic mistakes in evaluating the y-values given the x-values particularly when students are evaluating the negative exponents in the exponential function. Force x^2 coordinates into an |x| form when connecting the points.
 * Develop**: Have two tables of points or values. Have students graph the points. They will form a linear, absolute value, exponential and quadratic graph. Students will be responsible for compare and contrast features and the domain and range.

Level: Procedures with Connections: Represented in multiple ways and engage with conceptual ideas that underlie the procedures. Anticipation: f(x) notation, how to use f(x+2) to evaluate f(x)=x^2. Domain and range will be mixed up. Range will be something other than all real numbers. When graphing in a calculator they will need to know that the f(x) from the worksheet is the same as y. Students will probably need some group instruction when they are asked to connect the symbols a, h and k with the constant terms they used. Level: As above. This will be part 2 of the activity.
 * Solidify** Activity 1: Graph various quadratic equations of the form.
 * Solidify** Activity 2: Graph various quadratic equations with all the transformations mixed together.

Level: Procedures with Connections/Doing Mathematics (3.5): Making connections among multiple representations helps develop meaning. Require students to explore and understand the nature of the mathematical concepts processes or relationships. Require students to analyze the task and actively examine task constraints that may limit possible solution strategies. Require students to access relevant knowledge and experience and make appropriate use of them in working through the task. Anticipation: Linking the graph that they created to the contextual ideas presented in the situation. Connecting the words from the context to the mathematical terminology.
 * Practicing/Developing** Activity 1: Students will be asked to identify the key features of graphs that they sketch by hand and then verify the shape in a graphing calculator. Using the graphing calculator they will identify the meaning of the key features in relation to a contextual situation for which the graph is a model.