Lesson 12: 9-2 Transformations of Quadratic Functions

What happens when you add 5 to a quantity?
What happens to the vertex of a parabola when you add 5 to the y-coordinate?
Compare the graphs of y=ax^2 when a>0 and when a <0.

Vertex form
Horizontal translations

F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima
F.BF.3 Identify the effects on the graph of replacing f(x) by f(x)+k, kf(x), f(kx), and f(x+k) for specific values of k (both positive and negative); find the value of k given the graphs.

SAT questions related to solving quadratrics: 2-3-13,3-3-14,1-3-16,5-3-3,8-3-16,1-4-25; analyzing graphs: 3-4-12,8-3-11,8-4-19,6-3-11")

A family of functions is a group of functions whose graphs share the same basic characteristics. The parent graph is the simples graph in a family. All other graphs in the family are transformations of the parent function. Translations, dilations, and reflections can be preformed on the parent function of quadratics.

The path of center of gravity of a dancer during a leap can be modeled by g(x)=-0.17(x-3)^2 + 1.53, where x is the horizontal distance in feet of the center of gravity from th estarting point and h(x) is the vertical distance in feet. Describe the transformation in g(x) as it relates to the graph of the parent function.

The graph of f(x) = -ax^2 can result in two transofrmations of the graph of f(x) = x^2; a reflection across the x-axis if a>0 and either a compressions or expension depending on the absolute value of a.

If students need help comparing and contrasting a funcion's graph and it's parent function's graph, then have students write and graph three different functions on the same coordinate plane. Using a red pencil, on this same coordinate plane, have students the parent functions f(x) = x^2. Finally, have students creat obesrvation notebooks in which to recorde their thoughts on how each function's graph is similar to or different from the parent fucntion's graph.

Practice: Exercises 1 -9

Exercises 42-46

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