Transformations of Quadratic Functions in Standard and Vertex Form
1 Independent Practice
Using a graphing calculator, students will create 3 parabolas of various heights and widths by altering the a, b and c values of the equations and 3 parabolas by altering the h and k values. The students will follow the questions that correspond with the activity to help them think of the best equations to use.
2 Direct Instruction
I will go to the website: http://www.softschools.com/math/algebra/quadratic_functions/quadratic_fu...
This website has an interactive manipulative that allows you to change the different parts of the equation. Students will be able to draw conclusions as to how a graph is affected by changing a certain number in the equation.
3 Guided Practice
I will put a picture of a graph on the board and in groups, students will determine the best equation for this graph using their knowledge of direction of opening, width, y-intercept, and vertex.
4 Wrap Up
Students will perform a gallery walk. Students will display their graphs and equations on their desks while their classmates walk around to see how similar and different these are from their own.
Key Standards Supported
Write a function that describes a relationship between two quantities.
Determine an explicit expression, a recursive process, or steps for calculation from a context.
Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.
(+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.★
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.
Find inverse functions.
Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x3 or f(x) = (x+1)/(x–1) for x ≠ 1.
(+) Verify by composition that one function is the inverse of another.
(+) Read values of an inverse function from a graph or a table, given that the function has an inverse.
(+) Produce an invertible function from a non-invertible function by restricting the domain.
(+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.