Learning Objectives:

__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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