Properties Of The Graph Of A Quadratic Function Worksheet
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4Name: ____________________________________
Date: __________________
Properties of the Graph of a Quadratic Function
Algebra 1
Today we will begin our discussion of quadratic functions. Quadratic functions are useful in many
different areas, including the constructions of arches, modeling the flight of a golf ball, and
determining the path of hanging cables that support weight. Today we will begin by looking at their
graphs and properties.
th
Exercise #1: The 4
of July fireworks show in Cow Town USA can be modeled by the equation
= −
+
+
2
h
3.8
t
48.7
t
1.1.
If the rocket will explode at its highest point, at approximately what time, t ,
will the rocket explode? At approximately what height will the rocket explode?
h (ft)
160
100
60
20
t (sec)
0
2
4
6
8 10 12 14
The equation in Exercise #1 is an example of a quadratic function.
=
+
+
2
Definition: A quadratic function is an equation that can be placed in the form
y ax
bx c
a ≠ . This is called the standard form of a quadratic function. The graph of a quadratic
where
0
function is called a parabola .
Now let’s look at some properties of the quadratic function.
=
+
− and
2
Exercise #2: Using your calculator to generate xy -tables, graph the functions
y
x
2
x
3
= −
+
+ on the axes below.
2
y
x
4
x
2
y
y
x
x
What do we notice about these two graphs?
Algebra 1, Unit 5 – Quadratic Functions – L1
The Arlington Algebra Project, LaGrangeville, NY 12540
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