Applications of Quadratics

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)

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?

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?

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?

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)

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)

What is the highest point over the water?

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

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?

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?

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?

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