Algebra 1B
Name:________________________
Date:_________________________
Properties of Quadratic Functions
Remember:
 A quadratic function is any function having the form f(x) = ax2 + bx + c.
 The graph of a quadratic function is always a parabola
Zeros
Vertex
Axis of Symmetry
I. Here is a table for a quadratic function.
x
y
–7
–9
–6
–5
7
–4
–3
15
–2
16
–1
15
0
12
1
2
0
3
a. Graph all of the points, where you are given both the x and y coordinates.
b. Which of the points you’ve drawn must be the vertex of the parabola? Circle it on your
graph and label it vertex. Also write the coordinates of the vertex below.
Vertex = ( _____, ______)
c. Draw the axis of symmetry line.
d. What is the equation for the axis of symmetry line?
e. Graph the “mirror image” point of each point drawn in part a, if not already graphed.
f. Draw the parabola graph. (CONNECT THE DOTS.)
g. Fill in the missing y-values in the table.
h. Would the “a” of the equation for this parabola be positive or negative?
i. What are the zero(s) of the graph?
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II. Here is another quadratic function table.
x
f(x)
0
1
0
2
3.5
3
4
7.5
5
8
6
7.5
7
6
8
9
10
–4.5
a. What point is the vertex?
b. What are the zero(s)?
c. Fill in the missing numbers in the table.
III. Here is part of the table of a quadratic function. The vertex is (3, –8). Fill in the remaining
spaces with other points that must also be part of the graph.
x
f(x)
–2
15
–1
8
0
1
1
–4
2
–7
3
–8
4
5
6
7
8
3
HOMEWORK: Graphs and Tables of Quadratic Functions
1. The following table represents a quadratic function.
a. Complete the table.
x
f(x)
-4
-3
6
-2
-1
-2
0
-3
1
-2
2
1
3
4
13
b. Graph the points from the tables on the axes below and complete the parabola.
c. Draw the axis of
symmetry.
the q
d. What is the equation for
axis of symmetry?
of the
e. What are the coordinates
vertex?
ma
f. Is the vertex a minimum or
maximum?
equation
g. Would the “a” from the
equation be positive or
negative?
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2. The graph of a quadratic function f(x) is shown.
a. What are the coordinates of the vertex?
b.
Is the vertex a minimum or maximum?
c. Draw the axis of symmetry.
d. What is the equation for the axis of symmetry?
e. In the function formula f(x) = ax2 + bx + c, is the
value of a positive or negative?
f. What are the zero(s) of the function?
3. Here is a quadratic function: f(x) = –2x2 – 8x – 8.
a. Is the parabola going to be smiling or frowning? How do you know?
b. Complete the table and graph the function.
x
–4
f(x)
–3
–2
–1
0
1
2
3
4
c. What are the coordinates of the vertex?
d. Is the vertex a maximum or minimum?
e. Draw the axis of symmetry.
f. What is the equation for the axis of symmetry?
g. What are the zero(s) of the function?
5
4. Here is a table of values for a quadratic function f(x), with a
few numbers missing.
a. What point is the vertex, and is it a minimum or a
maximum?
vertex:
(____, ____)
circle which: maximum
minimum
b. What is the equation for the axis of symmetry?
c. Fill in the missing numbers in the table.
d. In the function formula f(x) = ax2 + bx + c,
is the value of a positive or negative?
e. What are the zero(s) of the function?
x
f(x)
–5
–3.5
–4
0
–3
–2
4
–1
4.5
0
4
1
2.5
2
0
3
4
–8
5
–13.5
5. Answer these questions about the quadratic function f(x) = –2x2 + 8.
a. Make an input-output table and a graph. Use your calculator as little as possible.
x
f(x)
c. What are the (x, y) coordinates of the vertex?
d. How many x-intercepts does this graph have? What are the coordinates of the x-intercept
point(s)? How many y-intercepts does this graph have? What are the coordinates of the yintercept point(s)?
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