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### Chapter 10 Story Problems

### Chapter 10 Story Problems

### Chapter 10 Story Problems

### Chapter 10 Story Problems

### Chapter 10 Story Problems

### Chapter 10 Story Problems

### Chapter 10.1/2 Review

### Chapter 10 Minimum or Maximum?

### Chapter 10.1/2 Review

### Chapter 10 Story Problems

### Chapter 10

### Chapter 10.1/2 Review

Domain x values

Range y values

p. 633 #40 Find domain and range

y = 0.012x2

Range 0 <y< 12.288

Domain -32<x< 32

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).

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?

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?

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

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

Axis of symmetry

Vertex

Min or Max

Opens Up or Down

y = x2 + 4x + 4

(-2, 0)

Min

Up

Axis of symmetry

Vertex

Min or Max

Opens Up or Down

X = 0

(0, 6)

y = -2x2 + 6

Max

Down

.

Graph the equation.

Use the 2nd Calc key to solve.

Minimum Graph upward

Maximum Graph downward

y = -3x2 - 7x + 15

Minimum Graph upward

y = x2 - 5x + 6

y = -8x2 + 10x - 20

Maximum Graph downward

.

y = 4x2 - 5x - 25

Minimum Graph upward

Axis of symmetry

Vertex

Min or Max

Opens Up or Down

y = -4x2 - 3

(0, -3)

Max

No Solutions

Down

Axis of symmetry

Vertex

Min or Max

Opens Up or Down

X = -3

y = x2 + 6x + 9

(-3, 0)

Min

-3

Up

Axis of symmetry

Vertex

Min or Max

Opens Up or Down

X = 4.5

y = x2 – 9x + 14

( 4.5, -6.25)

Min

7, 2

Up

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

Solve the equation using the quadratic formula.

x2 + 4x + 1 = 0

X2 – 6x + 12 = 0

X2 – 6x + 9 = 0

-3.73 -0.27

No solutions

.

3

Axis of symmetry

Vertex

Min or Max

Opens Up or Down

y = 3x2 + 4

(0, 4)

Min

No Solutions

Up

Axis of symmetry

Vertex

Min or Max

Opens Up or Down

X =-1

y = x2 + 2x + 1

(-1, 0)

Min

-1

Up

Axis of symmetry

Vertex

Min or Max

Opens Up or Down

X =-3.5

y = -x2– 7x +8

(-3.5,44.75 )

Max

-8, 1

Down

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