Section 3.1 – Quadratic Functions
math 130
Definition:
A quadratic function is a function that can be written in the form of
f x   ax 2  bx  c , for any
real number a, b, c ; a  0 .
Definition
If a quadratic function is of the form
f x   ax 2  bx  c , we say that the function is in
STANDARD FORM.
“So …when you can easily identify a, b, c then the quadratic function is in standard form”
Definition
If a quadratic function is of the form
f  x   a x  h   k
2
, where a  0 is said to be in VERTEX
FORM.
Definition
The vertex of the quadratic function
f x   ax  h  k is given by h, k 
2
Example #1 – More definitions
Example #2
The quadratic function

f x   2x  2  3 is in VERTEX FORM.
2
REWRITE IN STANDARD FORM
1
Looking at
f  x   a x  h   k
2

What does the value
a
tell you about your parabola?

What does the value
h
tell you?

What does the value
k
tell you?
Example #3
Using transformations and with out the use of your graphing calculator, graph the following quadratic
function.
f x   
1
x  42  2
2
2
Example #4
Find the quadratic function that has the given vertex and whose graph passes through the given point.
a) Vertex is (0,0) and passing through (-2,8)
b) Vertex is (2,5) and passing through (3,7)
c) Vertex is (-3,-2) and passing through (0,8)
3
Graphing Quadratic Functions in Standard form
If a function is in standard form then to graph, you want to find ….
 VERTEX

CONCAVE UP or CONCAVE DOWN

Y-intercept and x intercept
Example #5
Graph the quadratic function f x   x 2  4 x  5
4
Example #6
Graph the function
f x   x 2  2 x  4
Example #6
Graph the function
f  x   2  5 x  3x 2
5