Quadratics Examples for Note

A
A firework is launched
and follows the path of
the following parabola.
Sketch the parabola on
the axes to the right.
Label the co-ordinates
of the vertex, xintercepts (zeros), and
y-intercept.
What is the maximum height of the firework?
What is the initial height of the firework?
After what time does the firework reach its
maximum height?
After how many seconds does the firework land on
the ground?
vertex
direction of
opening
y-intercept
x-intercepts /
zeros
equation of axis
of symmetry
x
-2
y
first differences
second differences
-1
0
1
2
3
4
5
6
7
8
Convert to
Standard Form
Convert to
Factored Form
Convert to
Vertex Form
B
A firework is launched
and follows the path of
the following parabola.
Sketch the parabola on
the axes to the right.
Label the co-ordinates
of the vertex, xintercepts (zeros), and
y-intercept.
After how many seconds does the firework reach
its maximum height?
After how many seconds does the firework land on
the ground?
What is the initial height of the firework?
What is the maximum height of the firework?
vertex
direction of
opening
y-intercept
x-intercepts /
zeros
equation of
axis of
symmetry
x
-3
y
first differences
second differences
-2
-1
0
1
2
3
4
5
6
7
Convert to
Standard Form
Convert to
Factored Form
Convert to
Vertex Form
C
A football is thrown in
the air and follows the
path of the following
parabola.
Sketch the parabola on
the axes to the right.
Label the co-ordinates
of the vertex, xintercepts (zeros), and
y-intercept.
What is the initial height of the football?
After how many seconds does the football land on
the ground?
What is the maximum height of the football?
After how many seconds does the football reach its
maximum height?
vertex
direction of
opening
y-intercept
x-intercepts /
zeros
equation of
axis of
symmetry
x
-2
y
first differences
second differences
-1
0
1
2
3
4
5
Convert to
Standard Form
Convert to
Factored Form
Convert to
Vertex Form
D
A diver jumps off a cliff
into the water below
and follows the path of
the following parabola.
Sketch the parabola on
the axes to the right.
Label the co-ordinates
of the vertex, xintercepts (zeros), and
y-intercept.
How many seconds is the diver under water?
After how many seconds does the diver reach its
maximum depth?
What is the maximum depth of the diver?
What is the initial height of the diver?
vertex
direction of
opening
y-intercept
x-intercepts /
zeros
equation of
axis of
symmetry
x
-1
y
first differences
second differences
0
1
2
3
4
5
6
7
8
9
Convert to
Standard Form
Convert to
Factored Form
Convert to
Vertex Form
E
A hamburger is thrown
from the stands onto
the ice at a Ottawa
hockey game and
follows the following
path.
Sketch the parabola on
the axes to the right.
Label the co-ordinates
of the vertex, xintercepts (zeros), and
y-intercept.
After how many seconds does the hamburger reach
its maximum height?
What is the initial height of the hamburger?
After how many seconds does the hamburger land
on the ground?
What is the maximum height of the hamburger?
vertex
direction of
opening
y-intercept
x-intercepts /
zeros
equation of
axis of
symmetry
x
-3
y
first differences
second differences
-2
-1
0
1
2
3
4
5
6
7
Convert to
Standard Form
Convert to
Factored Form
Convert to
Vertex Form
F
A soccer ball is kicked
down the field from the
goal box and follows
the path of the following
parabola.
Sketch the parabola on
the axes to the right.
Label the co-ordinates
of the vertex, xintercepts (zeros), and
y-intercept.
What is the initial height of the soccer ball?
After how many seconds does the soccer ball reach
its maximum height?
What is the maximum height of the soccer ball?
After how many seconds does the soccer ball land
on the ground?
vertex
direction of
opening
y-intercept
x-intercepts /
zeros
equation of
axis of
symmetry
x
-1
y
first differences
second differences
0
1
2
3
4
5
6
7
8
9
Convert to
Standard Form
Convert to
Factored Form
Convert to
Vertex Form
G
A yo-yo is played with
and follows the path of
the following parabola.
Sketch the parabola on
the axes to the right.
Label the co-ordinates
of the vertex, xintercepts (zeros), and
y-intercept.
What is the initial height of the yo-yo?
After how many seconds does the yo-yo reach its
minimum height?
What is the minimum height of the yo-yo?
After how many seconds does the yo-yo reach its
original height?
vertex
direction of
opening
y-intercept
x-intercepts /
zeros
equation of
axis of
symmetry
x
-2
y
first differences
second differences
-1
0
1
2
3
Convert to
Standard Form
Convert to
Factored Form
Convert to
Vertex Form