Applications of Quadratics

​Projectile motion is a commonly modeled by quadratic functions

​Applications of Quadratic

Labelling

Do IT NOW!

Label the following.

Drag labels to their correct position on the image

Vertex

x-intercept

y-intercept

Multiple Choice

If the a value is positive, which direction does the graph open?

• up
• down
• left
• right

Multiple Choice

If the a value is negative, which direction does the parabola open?

• up
• down
• left
• right

Learning Target:
I am learning to construct and interpret quadratic functions from given data points to model real-life phenomena, and describe key graph characteristics to explain the contextual situation the function represents.

Success Criteria :
I am successful when construct a quadratic function from data points, interpret its key graph characteristics, and explain how the graph models a real-life situation

y-intercept generally tells how high the object was initially
vertex x-coordinate tells WHEN the object reaches max height, y-oord IS max height
x-intercept tell us when the object is on the ground

When an object is thrown...

Labelling

Label the graphic organizer.

Drag labels to their correct position on the image

Maximum height

Time to reach the maximum height

Time to hit the ground

Starting height

Solution not in the domain

A ball is thrown into the air with an upward velocity of 100 ft/s.
Its height, h, after t seconds is given by the function  
h(t) = -16t² + 64t + 960.

Ball

Multiple Choice

A ball is thrown into the air with an upward velocity of 100 ft/s. Its height, h, after t seconds is given by the function  

h(t) = -16t² + 64t + 960.

What is the maximum height? (use Desmos)

• 960 feet

• 1008 feet

• 1024 feet

• 1152 feet

Multiple Choice

A ball is thrown into the air with an upward velocity of 100 ft/s. Its height, h, after t seconds is given by the function

h(t)= -16t² + 64t + 960. When did the ball hit the ground?

• 10 seconds

• 2 seconds

• 5 seconds

• 7 seconds

Math Response

A ball is thrown into the air with an upward velocity of 100 ft/s. Its height, h, after t seconds is given by the function  

h(t) = -16t² + 64t + 960.

Find h(1)

Type answer here

Correct Answer: 1008

Deg^°

Rad

A ball is thrown into the air with an upward velocity of 40ft/s. Its height h in feet after t seconds is given by the function :

h(t) = -16t² + 40t + 10

Ball

Multiple Choice

A ball is thrown into the air with an upward velocity of 40ft/s. Its height h in feet after t seconds is given by the function :

h(t) = -16t² + 40t + 10

How many seconds does it take the ball to reach its maximum height?

• 1.25 seconds

• 1.4 seconds

• 2.5 seconds

• 2 seconds

Multiple Choice

A ball is thrown into the air with an upward velocity of 40ft/s. Its height h in feet after t seconds is given by the function :

h(t) = -16t² + 40t + 10

From which height is the ball thrown?

• 50 feet

• 35 feet

• 10 feet

• 25 feet

Multiple Choice

The parabola shows the trajectory of a tennis ball that was hit with a tennis racket. What is the starting height of the tennis ball? (Click the picture to enlarge it)

• 3 feet - y-intercept

• 12 feet - vertex

• 1.5 seconds - vertex

• 3 seconds - x-intercept

Multiple Choice

The parabola shows the trajectory of a tennis ball that was hit with a tennis racket. How long di it take for the tennis ball to hit the ground? (Click the picture to enlarge it)

• 3 feet

• 12 feet

• 1.5 seconds

• 3 seconds

Multiple Choice

What is the highest point over the water?

• 8 meters

• 1 meter

• 1 second

• 8 seconds

Multiple Choice

How long did it take to reach highest point over the water?

• 8 meters

• 1 meter

• 1 second

• 8 seconds

Real World Scenarios

Fill in the Blank

The profit that a company makes selling an item (in thousands of dollars) depends on the price of the item (in dollars). If x is the price of the item, then the profit can be found using the function

$$y=-2x^2+24x-54$$

Graph this in Desmos.  
What is the profit when the price is zero? (number only, no $)

Fill in the Blank

The profit that a company makes selling an item (in thousands of dollars) depends on the price of the item (in dollars). If x is the price of the item, then the profit can be found using the function

$$y=-2x^2+24x-54$$

Graph this in Desmos.  
What prices give a profit of zero dollars? (number only, no $)

Fill in the Blank

The profit that a company makes selling an item (in thousands of dollars) depends on the price of the item (in dollars). If x is the price of the item, then the profit can be found using the function

$$y=-2x^2+24x-54$$

Graph this in Desmos.  
What price gives the maximum profit? (number only, no $)

Poll

The same company's profit can be calculated using all three forms:

Standard Form:

$$-2x^2+24x-54$$  
Factored Form:  $$-2\left(x-3\right)\left(x-9\right)$$  
Vertex Form:  $$-2\left(x-6\right)^2+18$$  
Which form is most useful for finding the maximum profit?

• Standard

• Factored

• Vertex

Poll

The same company's profit can be calculated using all three forms:

Standard Form:

$$-2x^2+24x-54$$  
Factored Form:  $$-2\left(x-3\right)\left(x-9\right)$$  
Vertex Form:  $$-2\left(x-6\right)^2+18$$  
Which form is most useful for finding the profit when the price is zero?

• Standard

• Factored

• Vertex

Poll

The same company's profit can be calculated using all three forms:

Standard Form:

$$-2x^2+24x-54$$  
Factored Form:  $$-2\left(x-3\right)\left(x-9\right)$$  
Vertex Form:  $$-2\left(x-6\right)^2+18$$  
Which form is most useful for finding the prices that give a profit of zero dollars?

• Standard

• Factored

• Vertex

Poll

How are we feeling about this?