 ## Tutoring on Graphing and Finding Equations of Transformed Quadratic and Exponential Functions

Learning Objectives:

#### Understand to Graph and Solve Equations of Transformed Quadratic and Exponential Functions.

Math tutoring on Graphing and Finding Equations of Transformed Quadratic and Exponential Functions

The basic equation of the Exponential Function is of the form f(x) = aˣ (where a is positive). In general, when we have an exponential in form f(x) = aˣ + k or f(x) = aˣ - k, then the graph will be moved up or down k units. A left or right shift is what happens when we make a change to the exponent. In general, if we have the function then the graph will be moved left c units if c is positive and right c units if c is negative. If a negative is placed in front of an Exponential Function, then it will be reflected over the x-axis. The basic equation of the quadratic function is of the form y = x². The vertex of the graph of y = x² is at (0, 0). If the vertex is at some other point on the graph, then a translation or a transformation of the parabola has occurred.  When a quadratic function is given in vertex form, y = a(x-h)² + k, it is easy to see the new location of the vertex is at (h, k). If a <0, then we have a reflection parallel to the x-axis. If | a |>1 then the graph is steeper than y = x².  If k >0 then the translation is up. If k <0 then the translation is down.

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Hook Questions:                                                                                                                                                                                             1. How do you describe a transformation?

2. How do you move a quadratic to the right?

3. How do you translate a function?

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