# Quadratic Functions

**Definition: **A quadratic function is a function
which can be put in the form

(General Form) or
(Standard or Vertex Form )

For a quadratic functions or :

0) The domain of a quadratic function is

1) Graph : **a (vertical) parabola
**

2) Opens

**up if**

3) Opens

**down if**

4) Vertex: with

and

5) The x- intercept (s) can be found by setting and solving for x .

6) The y- intercept an be found by setting and solving for y .

**Remark:**The above items can be used to sketch the graph of a quadratic function

**Examples:**

**Remark:** The conversion from vertex form to general
from is very easy. For conversion from general form to vertex form

we use the method of ** Completing Square .
**

**Example:**

**The Maximum and the Minimum of a Quadratic Function (Parabola):**

As was discussed above, the vertex of a parabola is with

and

a) If the parabola opens up, the vertex will be the lowest point and we say that the parabola has the minimum value

of at .

b) If the parabola opes down, the vertex will be the highest point and we say that the parabola has the maximum

value of at .

**Remark:**The coordinates of the vertex can be found by a graphing calculator .

**Examples:**

Application:

Application:

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