Applying and analysing quadratic functions

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? (Find axis of symmetry)

• 1.25 seconds

• 1.4 seconds

• 2.5 seconds

• 2 seconds

A stone is tossed from a bridge into the river below. Its path is represented by  $h=-2t^2+7t\ +\ 9$  , where  $h$  is the height in meters and  $t$  is the time in seconds.

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

Round your answer to the nearest hundredth.

Find the equation of the model of best fit for the set of data:

• f(x) = 2.7x + 1.2

• f(x) = 0.75x² + 0.45x + 1.95

• f(x) = x² + 2

• f(x) = 1.9(1.74)^x

A diver is standing on a platform above the pool. He jumps form the platform with an initial upward velocity of 8 ft/s. Use the formula: h(t) = −16 t² + 8t + 24

How high is the platform?

• .25 ft

• 24 ft

• 25 ft

• 8 ft

The function f(t) = -5t²+20t + 60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground?

• 4 seconds

• -2 seconds

• -6 seconds

• 6 seconds

A restaurant wants to increase the price of a milkshake that currently costs $6. The restaurant has an employee conduct an analysis to predict the effect of the increased price on the weekly profit from milkshake sales. Based on the data collected, the employee makes the following graph. 

The price that will earn the maximum weekly profit is:

• $204

• $250

• $1.00

• $8.00

• $2.00

The y-intercept shows.....

• the maximum height that the graph reaches.

• the time that the graph reaches ground level.

• the height that the object started at.

• the minimum height that the graph reaches.

If path of a projectile is modeled by: 
h(t) = -16t² + 20t +6, what is the height after 1 second? 

• 6 feet 
• 20 feet 
• 10 feet 
• 4 feet 

Which two of these real world examples represent parabolas?

• Shooting a basketball

• Rolling a ball on the ground

• The Gateway Arch (St. Louis)

• The Empire State Building (NYC)

Solve the word problem:  How high would you jump if the equation for jumping from a cliff is:    h(t) = -16t² + 8t + 24?

• 25
• 24
• 8
• 26