Math 20-1
Quadratic Functions and Equations: Lesson #1
Characteristics of Quadratic Functions
Objective: By the end of this lesson, you will be able to:
- Recognize and define a quadratic function
- Find key characteristics of a quadratic function: vertex, axis of symmetry, direction of
opening, maximum or minimum value, intercepts, domain, and range
A quadratic function has a defining equation that can be written in the form:
(This is called the ______________ ________ of a quadratic function.)
e.g. 1) Are the following quadratic functions or not?
a) y  x  22 x  3
b) f x   x 2  x  5
d) f x   x  2  3
c) y  2 x 3  6 x  25
2
The graph of a quadratic function is called a ___________________.
* See “Parts of a Parabola” foldable.
e.g. 2) Use a table of values to graph the quadratic function f x    x 2  4 x  4 .
x
-1
f x 
0
1
2
3
4
5
Then find the following characteristics of the quadratic function:
a) y-intercept
b) x-intercept(s)
Math 20-1
Quadratic Functions and Equations: Lesson #1
c) coordinates of vertex
d) equation of axis of symmetry
e) direction of opening
f) minimum or maximum value
g) domain
h) range
You can also use technology to help you find these characteristics of a quadratic function.
e.g. 3) Use your graphing calculator to find the following characteristics of the quadratic
function y  0.5x 2  1.25x  3 :
a) y-intercept
b) x-intercept(s)
c) coordinates of vertex
d) equation of axis of symmetry
Math 20-1
Quadratic Functions and Equations: Lesson #1
e.g. 4) A quadratic function has an axis of symmetry at x  3 and a range of y  1 .
a) What are the coordinates of the vertex?
b) How many x-intercepts does the graph have?
e.g. 5) A quadratic function has x-intercepts of -7 and 4. What is the equation of the axis of
symmetry?
e.g. 6) A quadratic function has a vertex at (2, -5) and one x-intercept of -1. Determine the other
x-intercept and sketch the graph.
Assignment:
p. 174-175 #1-5, 8, 10