How long does a firework
stay in the air?
What is
the hang
time of a
football?
How does a satellite dish work?
Chapter 10 Quadratic Functions
Quadratic Functions are used to simulate real-life situations.
A quadratic function is an equation in the form:
y = ax2 + bx + c
10-1 Graphing Quadratic Functions
Objectives:
I will be able to graph a quadratic function.
I will be able to find the equation of the axis of
symmetry and the coordinates of the vertex.
The graph of a quadratic function is called a
parabola. It looks like a U or an upside down U.
4
f( x ) =
4
x 2-2× x-3
2
-5
f( x ) = (-x 2-2× x )+3
2
-55
5
-2
-2
-4
-4
Gallileo was the first to show that the path
of an object thrown in space is a parabola.
Graphing A Parabola
To graph a parabola we create a table of values and then
plot the points. Lets Graph: y = x2 – 2x – 3
x
-2
-1
0
1
2
3
4
y = x2 – 2x – 3
y
Graphing A Parabola
y = x2 – 2x – 3
x
y
-2
5
-1
0
0
-3
1
-4
2
-3
3
0
4
5
Graphing A Parabola
Lets Graph: y = -x2 + 2x + 1
x
-1
0
1
2
3
y = -x2 + 2x + 1
y
Graph It!
y = -x2 + 2x +1
x
y
-1
0
1
-2
1
2
2
3
1
-2
Parabola Characteristics
Quadratic Equation: y = ax2 + bx + c
– The maximum or minimum point is called the
vertex.
– If a is positive the graph opens up. (Minimum)
– If a is negative the graph opens down.(Maximum)
– The line that divides a parabola directly in half is
called its axis of symmetry.
– The axis of symmetry and vertex (turning point)
can be found using the equation
b
x
2a
The cables that act as suspension are parabolas.
Golden Gate Bridge
The general parabola equation is:
y = ax2 + bx + c
Lets look at the equation:
y = -x2 + 4x – 1
a = -1
Vertex is at
b=4
b
 (4)
4
x


2a
2(1)
2
y = -x2 + 4x – 1
x
y
2
c = -1
y = -x2 + 4x – 1
x
0
1
2
y
-1
2
3
3
4
2
-1
Vertex?
Max or Min?
Axis of Symmetry?
The general parabola equation is:
y = ax2 + bx + c
Lets look at the equation:
y = x2 – 2x – 8
a=1
Vertex is at
b = -2
 b  (2)
2
x


2a
2(1)
2
y = x2 – 2x – 8
x
y
1
c=-8
y = x2 – 2x – 8
x
-1
0
1
y
-5
-8
-9
2
3
-8
-5
Vertex?
Max or Min?
Axis of Symmetry?
Homework
Graphing Parabolas Homework #1