Chapter 10 Story
Problems
Domain x values
Range y values
Chapter 10 Story
Problems
Domain x values
Range y values
p. 633 #40 Find domain and range
y = 0.012x2
Domain -32< x < 32
Range
0 < y < 12.288
Chapter 10 Story Problems
Falling Objects - Two acorns drop from an oak tree.
One falls 45 feet while the other falls 32 feet.
Write an equation. h = -16t2 + vt + s
h = -16t2 + 46
h = -16t2 + 32
Graph the equations and compare.
The vertex is (0,46) and the other is (0, 32).
Chapter 10 Story Problems
Falling Objects - A pinecone falls about 25 feet from the
branch of the tree. How long does it take to land on the
ground?
Write an equation. h = -16t2 + vt + s
h = -16t2 + 25
0 = -(4t – 5)(4t +5)
t = 1.25 sec.
Graph the equation.
Where does it cross the x-axis?
Chapter 10 Story Problems
Suspension Bridges - p. 637 #4 The cables between the
Towers form a parbola with the equation y= 0.00014x2
-0.4x + 507 What is the height above the water at the
-lowest point?
X = -b/2a
X = -(-0.4)/2(0.00014) = 1428.6
Y = 0.00014(1428.6)2 – 0.4(1428.6) + 507 = 221 ft.
Graph the equation.
Where does it cross the x-axis?
Chapter 10 Story Problems
Architecture - p. 639 #41 The parabolic arches that support
The Convention Center can be modeled by the equation
Y = -0.0019x2 + 0.71x What is the highest point?
Graph the equation.
What are looking for? Vertex? X-intercept?
.
Use the 2nd Calc key to solve.
About 66 feet
Chapter 10 Story Problems
Architecture - p. 639 #41 The parbolic arches that support
The Convention Center can be modeled by the equation
Y = -0.0019x2 + 0.71x What is the highest point?
Graph the equation.
What are looking for? Vertex? X-intercept?
.
Use the 2nd Calc key to solve.
About 66 feet
Chapter 10.1/2 Review
y = x2 + 4x + 4
y = -2x2 + 6
.
Axis of symmetry X = -2
Vertex
(-2, 0)
Min or Max
Min
Opens Up or Down Up
Axis of symmetry X = 0
Vertex
(0, 6)
Max
Min or Max
Opens Up or Down Down
Graph the equation.
Use the 2nd Calc key to solve.
Chapter 10
Minimum or Maximum?
y = 5x2 + 3x + 12
Minimum Graph upward
y = -3x2 - 7x + 15
Maximum Graph downward
y = x2 - 5x + 6
Minimum Graph upward
y = -8x2 + 10x - 20 Maximum Graph downward
.
y = 4x2 - 5x - 25
Minimum Graph upward
Chapter 10.1/2 Review
y = -4x2 - 3
No Solutions
y = x2 + 6x + 9
-3
y = x2 – 9x + 14
7, 2
Axis of symmetry X = 0
(0, -3)
Vertex
Min or Max Max
Opens Up or Down Down
Axis of symmetry X = -3
Vertex
(-3, 0)
Min
Min or Max
Opens Up or Down Up
Axis of symmetry X = 4.5
Vertex
( 4.5, -6.25)
Min or Max Min
Opens Up or Down Up
Chapter 10 Story Problems
Sports Event – During an ice hockey game, a blimp flies 45 ft.
above the crowd and drops a numbered ball. The number
on the ball corresponds to a prize. Find the amount of time
in the air.
Graph the equation.
What are looking for? Vertex? X-intercept?
.
h = -16t2 + vt + s
About 1.7 sec
Chapter 10
Solve the equation using the quadratic formula.
1) x2 + 4x + 1 = 0
-3.73 -0.27
2) X2 – 6x + 12 = 0
No solutions
3) X2 – 6x + 9 = 0
3
.
Chapter 10
Solve the equation.
1) 2x2 – 20 = 78
7, -7
2) 3x2 – 7x + 2 = 0
.33, 2
3) 5x2 – 4x = 2
-.35, 1.15
.
Chapter 10
Linear, Quadratic, or Exponential Function?
X
-1
0
1
2
Y
3
0
3
12
X
0
1
2
3
Y
-5
-2
1
4
X
1
2
3
4
Y
1
2
4
8
Quadratic
Linear
.
Exponential
Chapter 10.1/2 Review
y = 3x2 + 4
No Solutions
y = x2 + 2x + 1
-1
y = -x2 – 7x + 8
-8, 1
Axis of symmetry X = 0
(0, 4)
Vertex
Min or Max Min
Opens Up or Down Up
Axis of symmetry X = -1
Vertex
(-1, 0)
Min
Min or Max
Opens Up or Down Up
Axis of symmetry X = -3.5
Vertex
( -3.5,44.75 )
Min or Max Max
Opens Up or Down Down
Chapter 10
Solve the equation.
1) 2x2 – 20 = 0
3.16, -3.16
2) x2 – 2x = 15
-3, 5
3) 5x2 – 7x = -1
.16, 1.24
.
Chapter 10
Linear, Quadratic, or Exponential Function?
X
-1
0
1
2
Y
1
0
1
4
X
0
1
2
3
Y
3
6
9
12
X
1
2
3
4
Y
1
2
4
8
Quadratic
Linear
.
Exponential