• Graph quadratic functions.
• Find the equation of the axis of symmetry and the
coordinates of the vertex of a parabola.
• quadratic function
• vertex
• parabola
• symmetry
• minimum
• axis of symmetry
• maximum
Graph Opens Upwards
Use a table of values to graph y = x2 – x – 2.
Graph these ordered pairs and connect
them with a smooth curve.
Answer:
Use a table of values to graph
y = x2 + 2x + 3.
0%
A.
B.
C.0%
D.
A
B
0%
C
D
0%
D
D.
C
C.
B
B.
A
A.
Graph Opens Downward
A. ARCHERY The equation y = –x2 + 6x + 4
represents the height y of an arrow x seconds after it
is shot into the area. Use a table of values to graph
y = –x2 + 6x + 4.
Graph these ordered pairs and connect them with a
smooth curve.
Answer:
Graph Opens Downward
B. What are the mathematical domain and range of
the function? Describe reasonable domain and
range values for this situation.
Answer: D: {x | x is a real number}
R: {y | y ≤ 13}
The arrow is in the air for about 6.6 seconds, so
a reasonable domain is D: {x | 0 < x < 6.6}. The
height of the arrow ranges from 0 to 13 feet, so
a reasonable range is R: {y | 0 < y < 13}.
Use a table of values to graph y = –x2 + 4.
A.
B.
C.
D.
1.
2.
3.
4.
A
B
C
D
0%
A
B
C
D
Vertex and Axis of Symmetry
A. Consider the graph of y = –2x2 – 8x – 2. Write the
equation of the axis of symmetry.
In y = –2x2 – 8x – 2, a = –2 and b = –8.
Equation for the axis of
symmetry of a parabola
a = –2 and b = –8
Answer: The equation of the axis of symmetry is x = –2.
Vertex and Axis of Symmetry
B. Consider the graph of y = –2x2 – 8x – 2. Find the
coordinates of the vertex.
Since the equation of the axis of symmetry is x = –2
and the vertex lies on the axis, the x-coordinate for the
vertex is –2.
y = –2x2 – 8x – 2
Original equation
y = –2(–2)2 – 8(–2) – 2
x = –2
y = –8 + 16 – 2
Simplify.
y=6
Add.
Answer: The vertex is (–2, 6).
Vertex and Axis of Symmetry
C. Consider the graph of y = –2x2 – 8x – 2. Identify
the vertex as a maximum or minimum.
Answer: Since the coefficient of the x2 term is negative,
the parabola opens downward and the vertex
is a maximum point.
Vertex and Axis of Symmetry
D. Consider the graph of y = –2x2 – 8x – 2. Graph
the function.
You can use the symmetry of the
parabola to help you draw its graph.
On a coordinate plane, graph the
vertex and the axis of symmetry.
Choose a value for x other than –2. For
example, choose –1 and find the ycoordinate that satisfies the equation.
y = –2x2 – 8x – 2
y = –2(–1)2 – 8(–1) – 2
y=4
Original equation
x = –1
Simplify.
Vertex and Axis of Symmetry
D. Graph the function.
Graph (–1, 4).
Since the graph is symmetrical
about its axis of symmetry
x = –2, you can find another
point on the other side of the
axis of symmetry. The point
at (–1, 4) is 1 unit to the right of
the axis. Go 1 unit to the
left of the axis and plot the point
(–3, 4).
Vertex and Axis of Symmetry
D. Graph the function.
Repeat this for several other points.
Then sketch the parabola.
A. Consider the graph of y = 3x2 – 6x + 1. Write the
equation of the axis of symmetry.
A. x = –6
0%
B. x = 6
C. x = –1
1.
2.
3.
4.
A
D. x = 1
A
B
C
D
B
C
D
B. Consider the graph of y = 3x2 – 6x + 1. Find the
coordinates of the vertex.
A. (–1, 10)
0%
B. (1, –2)
C. (0, 1)
D. (–1, –8)
1.
2.
3.
4.
A
A
B
C
D
B
C
D
C. Consider the graph of y = 3x2 – 6x + 1. Identify the
vertex as a maximum or minimum.
A. minimum
0%
B. maximum
C. neither
1.
2.
3.
4.
A
D. cannot be determined
A
B
C
D
B
C
D
D. Consider the graph of y = 3x2 – 6x + 1. Graph the
function.
A.
B.
C.
D.
1.
2.
3.
4.
A
B
C
D
A
0%
B
C
D
Match Equations and Graphs
Which is the graph of y = –x2 – 2x –2?
A
B
C
D
Match Equations and Graphs
Read the Test Item
You are given a quadratic function, and you are asked
to choose its graph.
Solve the Test Item
Find the axis of symmetry of the graph y = –x2 – 2x – 2.
Equation for the axis of
symmetry
a = –1 and b = –2
Match Equations and Graphs
The axis of symmetry is –1. Look at the graphs. Since
only choices C and D have x = –1 as their axis of
symmetry, you can eliminate choices A and B. Since
the coefficient of the x2 term is negative, the graph
opens downward. Eliminate choice C.
Answer: D
Which is the graph of y = –x2 + 2x?
0%
A.
B.
0%
C.
D.
A
B
0%
C
D
0%
D
D.
C
C.
B
B.
A
A.