Section 9.1
Graphing Quadratic
Functions
Standard 21.0 Students graph quadratic functions
and know that their roots are the x-intercepts.
• Graph quadratic functions.
• Find the equation of the axis of symmetry and the
coordinates of the vertex of a parabola.
•
•
•
•
quadratic function
parabola
minimum
maximum
• vertex
• symmetry
• axis of symmetry
The graph of a quadratic function is called a parabola.
If a is positive, then the parabola opens upward.
If a is negative, then the parabola opens downward.
The graph of a quadratic function is called a parabola.
If a is positive, then the parabola opens upward.
If a is negative, then the parabola opens downward.
A wider parabola has a leading coefficient closer to 0.
A narrower parabola has a leading coefficient farther from 0.
The vertex is the point where the parabola changes direction. It
can be either a maximum or a minimum. (x, y) or (h, k)
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:
The lowest point of a parabola is called the minimum.
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:
The highest
point of a
parabola is
called the
maximum.
Parabolas have symmetry.
• Symmetrical figures are those in which each half of the
figure matches the other exactly.
• The line of symmetry cuts a parabola in half.
𝑏
• The equation for the line of symmetry is 𝑥 = − .
2𝑎
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. (x, y)
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.
A. Consider the graph of y = 3x2 – 6x + 1. Write the
equation of the axis of symmetry.
A. x = –6
B. x = 6
C. x = –1
D. x = 1
B. Consider the graph of y = 3x2 – 6x + 1. Find the
coordinates of the vertex.
A. (–1, 10)
B. (1, –2)
C. (0, 1)
D. (–1, –8)
C. Consider the graph of y = 3x2 – 6x + 1. Identify the
vertex as a maximum or minimum.
A. minimum
B. maximum
C. neither
D. cannot be determined
D. Consider the graph of y = 3x2 – 6x + 1. Graph the
function.
A.
B.
C.
D.
Match Equations and Graphs
Which is the graph of y = –x2 – 2x –2?
A
B
C
D
Homework Assignment #56
9.1 Skills Practice Sheet