Section 6 Graph Quadratic Equations

1
Chapter 9

• Section 6 Graph Quadratic Equations

2
Graphs of Quadratic Equations

• Graphs of quadratic equations
• have a parabolic shape.

3
Parabolas Out in the Real World

• Source http//www.pen.k12.va.us/Div/Winchester/j
  hhs/math/lessons/calc2004/appparab.html

4
Braking Distance Formulas
5
Graph of Total Stopping Distance
Formula Used
6
Radiant Heaters
Heat Source
Heat is concentrated in parallel rays.
7
Headlights
Glass reflector with bright aluminum deposited.
8
Headlights
9
Parabolic Reflectors
A person standing at the focus of this parabola
can hear a whisper from the person at the other
parabola.
10
Terminology
11
Terminology involving Parabolas

• A parabola will open either
• Upward or..
• Downward

12
Terminology involving Parabolas
The parabola will be symmetric with respect to an
axis of symmetry.
13
Terminology involving Parabolas
The point where the parabola intersects its axis
of symmetry is called the vertex.
vertex
?
?
vertex
14
Graphing Equations of the form y ax2
15
Graphing
y-axis
Axis of Symmetry _______
(0,0)
Vertex _______

• Graph

?
?
(-2,4)
-2
4
?
?
(-1,1)
-1
1
?
(0,0)
0
0
1
(1,1)
1
4
2
(2,4)
16
Graphing
y-axis
Axis of Symmetry _______
(0,0)
Vertex _______

• Graph

y
(-4,-8)
-4
-8
?
x
(-2,-2)
-2
-2
?
?
(0,0)
0
0
-2
(2,-2)
2
-8
4
(4,-8)
?
?
17
Graphing Equations of the Form y ax2 bx
c
18
Graphing

• Given a quadratic equation, of the form
  y ax2 bx c
• Use the same techniques

?
?
?
Hard to tell where the axis of symmetry lies and
where the vertex is at.
?
?
?
19
Graphing Points of Interest
vertex
y-intercept
?
?
?
?
x-intercept
x-intercept
20
Graphing Points of Interest Vertex

• Graph

y
The x-coordinate of the vertex is found using
this
x
?
21
Graphing Points of Interest Vertex

• Graph

y
The y-coordinate of the vertex is by substituting
the x-value into the equation
x
?
22
Graphing Points of Interest y-intercept

• Graph

y
?
?
(-4,0)
-4
0
(-3,-5)
-3
-5
x
(0,-8)
0
-8
?
?
1
-5
(1,-5)
y-intercept
2
0
(2,0)
?
?
23
Graphing Points of Interest Intercepts

• Graph

y
Find all the y and x-intercepts of the graph.
y-intercept
x
?
24
Graphing Points of Interest

• Graph

y
Find all the y and x-intercepts of the graph.
x-intercept
?
?
x
?
25
Recap Points of Interest

• Given an equation of the form

Vertex
x-coordinate
y-coordinate
Substitute x-coordinate value into original
equation, solve for y.
?
?
?
?
y-intercept
Let x 0, solve for y.
x-intercepts
Let y 0, solve for x.
26
Recap Points of Interest

• Given an equation of the form

Plot other points to determine the final shape.
Vertex
x-coordinate
y-coordinate
Substitute x-coordinate value into original
equation, solve for y.
?
?
y-intercept
Let x 0, solve for y.
27
Graphing One More

• Graph

Establish the vertex location
x-coordinate
Vertex (1,3)
?
y-coordinate
28
Graphing One More

• Graph

y-intercept
?
0
1
(0,1)
1
(2,1)
2
?
?
3
-5
(3,-5)
etc.
etc.
etc.
?
?
29
Practice

• MathXL Ch 9 Section 6 Homework