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Chapter  10-­‐2:  Graphs  of  Quadra-c  Func-ons So we’ve spent the better part of the semester learning how to factor, solve, and manipulate quadratic equations. But what do they actually LOOK like? Back in the day (3rd Quarter), we looked at basic graphs of several functions. The one we will focus on for the time being is the quadratic function which takes the shape of a _________________.

This is the graph of the ________________ function, ___________________.

The DOMAIN of all quadratic functions is __________. The range depends on the _____________ and the __________________ of the graph.

A function that can be written in the form __________________________ for real numbers a, b, and c with ____________ is called a ____________________ function.

However....the standard form is not the best way to graph a quadratic function. It is easier to see how to graph a function in terms of transformations of the parent function.

Graph the Parent Function - Use a Table of Values

x

f(x)


Types of Transformations Vertical Shift If you ____________ a number to the parent function ______________ to make it _________________, then you have translated the graph ____ ____________ up or down. Example 1: Graph

f (x) = x 2 + 3 . State the transformation. Give the vertex, domain, and range.

Graph

f (x) = x 2 − 5 . State the transformation. Give the vertex, domain, and range.


Horizontal Shift If you ____________ a number to the _______ value in the parent function ______________ to make it _________________, then you have translated the graph ____ ____________ left or right. Example 2: Graph

f (x) = (x + 2)2 . State the transformation. Give the vertex, domain, and range.

Graph

f (x) = (x − 3)2 . State the transformation. Give the vertex, domain, and range.


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