**A linear function ** ,f of x, can be written in the
form f(x)=ax+b, where a and b are real numbers. The graph of a linear function
is a **nonvertical linea** with slope a and y -intercept (0,b)

**Problem Type #1:** Consider the fol lowing linear
function. Reduce all fractions to lowest terms.

1) Find the slope and y-intercept (entered as an ordered
pair ) of the line which is represented by this function.

2) Graph this linear function by finding two points on the
line. (Note: You can use the y- intercept as one of the points .)

**EX1:**

**EX2:**

**EX3:**

A ** quadratic function ** ,f of x, can be written in the
form where a, b, and c are real numbers and
a ≠0. The graph of a quadratic function is a** parabola**.

The **vertex form** of a quadratic function is
.

(Vertex form can be arrived at by ** completing the square ** or by using the
** Vertex Formula **.)

The graph of f is a **parabola** with **vertex**
(h,k) and **axis of symmetryhx x=h**

The parabola **opens up** a>0 if with the function
having a **minimum** value at k.

The parabola a >0 a>0 if with the function having a **
maximum** value at k .

**The Vertex Formula**

The **vertex** of the graph of

**Problem Type #2 :**Consider the following quadratic
function

Reduce all fractions to the lowest terms . :

1) Find the vertex of this function.

2) Enter the x-intercept(s), if any, of this function as ordered pair(s).

3) Graph this quadratic function by identifying two points on the parabola other
that the vertex and the x-intercept(s).

**EX4:**

**EX5:**

**EX6:**

**4.2b MAX/MIN APPLICATIONS OF QUADRATIC FUNCTIONS**

**Problem Type #1:**

**EX1:**

A small cruising ship that can hold up to 56 people provides three-day
excursions to groups of 36 or more. If the group contains 36 people, each person
pays $62. The cost per person is reduced by $1 for each person in excess of 36.
Find the size of the group that maximizes income for the owners of the ship.

**Problem Type #2:**

**EX2:**

A rancher has 400 feet of fencing to put around a rectangular field and then
sub divide the field into 3 identical smaller rectangular plots by placing two
fences parallel to one of the field’s shorter sides. Find the dimensions that
maximize the enclosed area.