Warm Up

Find five points and use them to graph

Hint, use an x-y table to help you 
y  x2
11-1 GRAPHING QUADRATIC
FUNCTIONS
Objective: To find and use the axis of
symmetry and the vertex of a parabola to
graph it.
Standard 21.0
GRAPH FOR WARM UP
This “U” shape is called a parabola.
Magic Ordered Pairs
(1,1a) (2,4a) (3,9a)
Use these every time
When A,B,C change,
moves vertex but does
not change the shape
Quadratic Function: y = Ax2 + Bx + C
A,B,C are integers
Vertex
Turning point
(0,0)
On axis of symmetry
Axis of Symmetry
Cuts parabola in half
Reflects over line
x=0
b
x
2a
Looks like..

A parabola can also make

shape.
To tell which way it points, look at the a value
y  ax  bx  c
2

a (+) =
+ +

A (-) =
– –
minimum (vertex)
maximum (vertex)
Standard
Form
Examples
Opens
Up or
Down
Find the
axis of
symmetry
y = ax2 + bx + c a(+) = up/min x = – b
a(-) = down/max
2a
y = x2
“Parent function”
Find
the
vertex
Graph using
the parent
function
Plug in x to
standard
form
(1,1) (2,4)
(3,9) reflect
y = 1x2 + 0x + 0
x= 0
Up
a=1
2(1)
b = 0 Vertex
x=0
c=0
Minimum
y = (0)2
y=0
(0,0)
This is the same
graph as the
warm up!
“11-1 Graphing Quadratic Functions”
Worksheet
Follow along and fill in the worksheet with me.
 We will graph 3 parabolas today in class
 You will complete tonight’s homework on a
similar worksheet so…


Take good notes in class so you can use them to help
you do the homework! 
HOMEWORK

See problems below:
1) y = x2 + 4x + 3
2) y = -x2 + 4x – 1
3) y = x2 + 6x + 9
4) y = -x2 – 3
5) y = x2 – 4x

To be done on worksheet given in class

Answers include:
Up/down?
Min/Max?
Axis of Symmetry
Vertex
Graph
Extra Practice!

The following 2 parabolas can be graphed and
studied for extra practice 
Examples
Opens
Up or
Down
Standard
Form
ax2 + bx + c = y a(+) = up
a(-) = down
y = x2 – 2x – 3
Find
the
vertex
Graph using
the parent
function
x=–b
2a
Plug in x to
standard
form
(1,1) (2,4)
(3,9) reflect
Up
y = x2 – 2x – 3
a=1
b = -2
c = -3
Find the
axis of
symmetry
x = -(-2)
Vertex
2(1)
Minimum
x=1
y = (1)2 – 2(1) – 3
y=1–2–3
y = -4
(1,-4)
Examples
Opens
Up or
Down
Standard
Form
ax2 + bx + c = y a(+) = up
a(-) = down
y = x2 + 4x + 4
Find
the
vertex
Graph using
the parent
function
x=–b
2a
Plug in x to
standard
form
(1,1) (2,4)
(3,9) reflect
Up
y = x2 + 4x + 4
a=1
b=4
c=4
Find the
axis of
symmetry
x = -(4)
Vertex
2(1)
Minimum
x = -2
y = (-2)2 + 4(-2) + 4
y = 4 – 8 +4
y=0
(-2,0)