# 5.1 – Introduction to Quadratic Functions

Document Sample

```					5.1 – Introduction to
Quadratic Functions
Objectives: Define, identify, and graph quadratic
functions.
Multiply linear binomials to produce a
quadratic expression.
Standard: 2.8.11.E. Use equations to represent curves.
I. Quadratic function is any function that
can be written in the form f(x)= ax2 + bx + c,
where a ≠ 0.
   Ex 2. Let f(x) = (2x – 5)(x - 2). Show that f
represents a quadratic function. Identify
a, b, and c when the function is written
in the form f(x) = ax2 + bx + c.
   FOIL  First – Outer – Inner – Last

 (2x – 5)(x – 2) = 2x2 – 4x – 5x + 10
2x2 – 9x + 10
a = 2, b = -9, c = 10
   II. The graph of a quadratic function is called a
parabola.
   Each parabola has an axis of symmetry, a line that
divides the parabola into two parts that are mirror
images of each other.
   The vertex of a parabola is either the lowest point on
the graph or the highest point on the graph.
Axis of
Symmetry

Vertex
Example 1
Example 2
   Ex 2. Identify whether f(x) = -2x2 - 4x + 1 has a
maximum value or a minimum value at the vertex.
Then give the approximate coordinates of the
vertex.

   First, graph the function:

   Next, find the maximum value of the parabola (2nd,
Trace):

   Finally,
III. Minimum and Maximum
Values

   Let f(x) = ax2 + bx + c, where a ≠ 0.
The graph of f is a parabola.
 If a > 0, the parabola opens up and
the vertex is the lowest point. The y-
coordinate of the vertex is the
minimum value of f.
 If a < 0, the parabola opens down
and the vertex is the highest point.
The y-coordinate of the vertex is the
maximum value of f.
   Ex 1. State whether the parabola opens up or down
and whether the y-coordinate of the vertex is the
minimum value or the maximum value of the
function. Then check by graphing it in your Y =
button on your calculator. Remember: F(X) means
the same thing as Y!
   a. f(x) = x2 + x – 6   Opens up, has minimum value
   b. g(x) = 5 + 4x – x2 Opens down, has maximum value
   c. f(x) = 2x2 - 5x + 2 Opens up, has minimum value
   d. g(x) = 7 - 6x - 2x2 Opens down, has maximum value
   Homework: page 278 # 14-40 even

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 18 posted: 9/24/2012 language: English pages: 9