4.1: Do Now
John placed a container outside during a rainstorm.
A gauge on the side of the container shows the
height, in millimeters, of the water in the container.
The table below lists the height of water the gauge
showed along with the corresponding number of
hours after the rainstorm started. What is the average
rate of change, in millimeters per hour, of the height
of water in the container from time 2 hours to 5 hours?
Time (hours)
Height (millimeters)
a.
b.
c. 6
0
0
2
12
3
16
d. 8
5
32
7
42
Algebra II
4.1: Graphing Quadratic Equations,
HW: 4.1: p.240-242 (8, 12, 14, 22, 36, 38,
44-46 all, 58)
Quiz 4.1-4.2: TBD
4.1: Notes
 Quadratic




Equation:
Standard Form: y = ax2 + bx + c
Parabolic shape
Vertical line of symmetry
If a is positive parabola will go up, if a is
negative parabola will go down.
Notes
 Quadratic

Equation:
Through the line of symmetry is the vertex
which is either the maximum or minimum
value for the parabola.
• Vertex is maximum if parabola opens down.
• Vertex is minimum if parabola opens up.
Notes continued
 Quadratic


Equation continued. y = ax2 + bx + c
Equation for line of symmetry:
x-coordinate of vertex (find y-value by plugging in
x-value and solving:
Tell whether the function has a minimum
value or maximum value. Then find the
minimum or maximum value.
1.) y = -6x2 – 1
2.) f(x) = 2x2 + 8x + 7
Steps to graphing a quadratic equation
 Steps:
2
y = ax + bx + c
1.) Find the vertex.
2.) Graph using a table of values with the
vertex in the middle.
2
Graph y = -2x .
X
Y
2
Graph y = -x + 2.
X
Y
2
Graph y = -4x + 8x + 2.
X
Y
Do Now: p.242 #57
Do Now
The figure shows the graph of
the profit function for a
company. In the graph, y
represents the profit, in
thousands of dollars, that the
company earns for selling x
thousand items. Interpret the
meaning of the two intercepts
shown in the context of the
problem.
Algebra II
4.2: Graph quadratic function in vertex or
intercept form
HW: 4.2: p.249-251 (4, 8, 10, 16, 18, 34, 52, 54)
4.2: Vertex Form
= a(x – h) + k
 Vertex: (h, k)
 Graph using table
y
2
Graph y = 2(x – 4)2 – 1.
X
Y
Graph y = (x + 1)2 + 3.
X
Y
2
Graph y = 2(x + 1) + 3.
X
Y
4.2: Intercept form
 Steps
in graphing intercept form
y = a(x – p)(x – q)
Plot the x-intercepts: points p and q
 Find x-coordinate of vertex by averaging p
and q:


Find y-coordinate of vertex by plugging in
x-coordinate and solving. Plot the vertex.
Graph y = (x + 2)(x – 2) .
Graph y = 3(x + 3)(x + 5) .
p.247 example 4
3 types of graphs
2
1.) Stand. form: y = ax + bx + c
1.) x-coordinate of vertex:
2.) chart with vertex in the middle
2.) Vertex form: y = a(x – h)2 + k
1.) vertex: (h, k)
2.) chart with vertex in the middle
3.) Intercept form: y = a(x – p)(x – q)
1.) x-intercepts: p and q
2.) x-coordinate of vertex: average
p and q. Find y by plugging in.
Graph and
determine 1.)
the domain 2.)
and range. 3.)
4.)
5.)
6.)
7.)
8.)
2
y = 3x
y = (x – 4)(x – 2)
2
y = -2x + 5
2
y = ½x
2
y = (x – 2)
2
y = 3x + 6x – 4
y = ½(x + 1)(x – 2)
2
f(x) = -x - 2x - 1