Warm Up1. Order the following from widest to

narrowest: y = -2x2, y = 5x2, y = .5x2, y = -3.5x2

2. Find the vertex of y = -2x2 – 8x – 10.

3. Find the root(s) of y = 3x2 + 5x – 1.

4. Solve: 0 = -2x2 – 8x – 10.

Homework Solutions

Basketball parabola!http://www.youtube.com/watch?v

=dSRWY5vUHCU

Until 1:25

Quadratic modelingWe can create quadratic

functions to model real world situations all around us.

We can use these models to find out more information, such as:◦Minimum/maximum height◦Time it takes to reach the ground◦Initial height

Example #1:

For a typical basketball shot, the ball’s height (in feet) will be a function of time in flight (in seconds), modeled by an equation such as

h = -16t2 +40 t +6.a) What is the maximum

height of the ball? How long does it take to reach the maximum height?

To find maximum height:Are we looking for x or for y?Graph the function. Adjust xmin

and xmax, then press ZOOM 0.Find the vertex.

Example #2:The distance of a diver above the

water h(t) (in feet) t seconds after diving off a platform is modeled by the equation h(t) = -16t2 +8t +30.

a) How long does it take the diver to reach her maximum height after diving off the platform? What is her maximum height?

Example #3:The height, H metres, of a rocket

t seconds after it is fired vertically upwards is given by h(t) = -50t2 + 80t.

a) What is the highest point that the rocket reaches? When does it reach this point?

Example #1:

For a typical basketball shot, the ball’s height (in feet) will be a function of time in flight (in seconds), modeled by an equation such as

h = -16t2 +40 t +6.b) When will the shot reach

the height of the basket? (10 feet)

To find a time given height…Let y2 = given height. Find the intersection of y1 and y2

Example #2:The distance of a diver above the

water h(t) (in feet) t seconds after diving off a platform is modeled by the equation h(t) = -16t2 +8t +30.

b) When will the diver reach a height of 2 feet?

Example #3:The height, H metres, of a rocket

t seconds after it is fired vertically upwards is given by h(t) = -50t2 + 80t.

c) At what time(s) is the rocket at a height or 25 m?

Example #1:

For a typical basketball shot, the ball’s height (in feet) will be a function of time in flight (in seconds), modeled by an equation such as

h = -16t2 +40 t +6.c) When will the ball hit the

floor if it missed the basket entirely?

To find the time it takes it hit the ground…This is asking us when does the

height = 0? So what are we trying to do here?

Let y2 = 0.Find the intersection of y1 and y2

Example #2:The distance of a diver above the

water h(t) (in feet) t seconds after diving off a platform is modeled by the equation h(t) = -16t2 +8t +30.

c) When will the diver hit the water?

Example #3:The height, H metres, of a rocket

t seconds after it is fired vertically upwards is given by h(t) = -50t2 + 80t.

c) When will the rocket hit the ground?

Example #1:

For a typical basketball shot, the ball’s height (in feet) will be a function of time in flight (in seconds), modeled by an equation such as

h = -16t2 +40 t +6.d) What is the height of the

ball when it leaves the player’s hands?

To find the initial height…Find the y-intercept!

Example #2:The distance of a diver above the

water h(t) (in feet) t seconds after diving off a platform is modeled by the equation h(t) = -16t2 +8t +30.

d) How high is the diving board?

Example #3:The height, H metres, of a rocket

t seconds after it is fired vertically upwards is given by h(t) = -50t2 + 80t.

c) What was the initial height of the rocket?

Summarize