Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2...
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Transcript of Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2...
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