![Page 1: Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2 2. Find the vertex of y = -2x 2 – 8x – 10. 3. Find](https://reader036.vdocuments.net/reader036/viewer/2022062421/56649dd45503460f94acb93c/html5/thumbnails/1.jpg)
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.
![Page 2: Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2 2. Find the vertex of y = -2x 2 – 8x – 10. 3. Find](https://reader036.vdocuments.net/reader036/viewer/2022062421/56649dd45503460f94acb93c/html5/thumbnails/2.jpg)
Homework Solutions
![Page 3: Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2 2. Find the vertex of y = -2x 2 – 8x – 10. 3. Find](https://reader036.vdocuments.net/reader036/viewer/2022062421/56649dd45503460f94acb93c/html5/thumbnails/3.jpg)
![Page 4: Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2 2. Find the vertex of y = -2x 2 – 8x – 10. 3. Find](https://reader036.vdocuments.net/reader036/viewer/2022062421/56649dd45503460f94acb93c/html5/thumbnails/4.jpg)
Basketball parabola!http://www.youtube.com/watch?v
=dSRWY5vUHCU
Until 1:25
![Page 5: Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2 2. Find the vertex of y = -2x 2 – 8x – 10. 3. Find](https://reader036.vdocuments.net/reader036/viewer/2022062421/56649dd45503460f94acb93c/html5/thumbnails/5.jpg)
![Page 6: Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2 2. Find the vertex of y = -2x 2 – 8x – 10. 3. Find](https://reader036.vdocuments.net/reader036/viewer/2022062421/56649dd45503460f94acb93c/html5/thumbnails/6.jpg)
![Page 7: Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2 2. Find the vertex of y = -2x 2 – 8x – 10. 3. Find](https://reader036.vdocuments.net/reader036/viewer/2022062421/56649dd45503460f94acb93c/html5/thumbnails/7.jpg)
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
![Page 8: Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2 2. Find the vertex of y = -2x 2 – 8x – 10. 3. Find](https://reader036.vdocuments.net/reader036/viewer/2022062421/56649dd45503460f94acb93c/html5/thumbnails/8.jpg)
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?
![Page 9: Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2 2. Find the vertex of y = -2x 2 – 8x – 10. 3. Find](https://reader036.vdocuments.net/reader036/viewer/2022062421/56649dd45503460f94acb93c/html5/thumbnails/9.jpg)
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.
![Page 10: Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2 2. Find the vertex of y = -2x 2 – 8x – 10. 3. Find](https://reader036.vdocuments.net/reader036/viewer/2022062421/56649dd45503460f94acb93c/html5/thumbnails/10.jpg)
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?
![Page 11: Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2 2. Find the vertex of y = -2x 2 – 8x – 10. 3. Find](https://reader036.vdocuments.net/reader036/viewer/2022062421/56649dd45503460f94acb93c/html5/thumbnails/11.jpg)
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?
![Page 12: Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2 2. Find the vertex of y = -2x 2 – 8x – 10. 3. Find](https://reader036.vdocuments.net/reader036/viewer/2022062421/56649dd45503460f94acb93c/html5/thumbnails/12.jpg)
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)
![Page 13: Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2 2. Find the vertex of y = -2x 2 – 8x – 10. 3. Find](https://reader036.vdocuments.net/reader036/viewer/2022062421/56649dd45503460f94acb93c/html5/thumbnails/13.jpg)
To find a time given height…Let y2 = given height. Find the intersection of y1 and y2
![Page 14: Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2 2. Find the vertex of y = -2x 2 – 8x – 10. 3. Find](https://reader036.vdocuments.net/reader036/viewer/2022062421/56649dd45503460f94acb93c/html5/thumbnails/14.jpg)
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?
![Page 15: Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2 2. Find the vertex of y = -2x 2 – 8x – 10. 3. Find](https://reader036.vdocuments.net/reader036/viewer/2022062421/56649dd45503460f94acb93c/html5/thumbnails/15.jpg)
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?
![Page 16: Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2 2. Find the vertex of y = -2x 2 – 8x – 10. 3. Find](https://reader036.vdocuments.net/reader036/viewer/2022062421/56649dd45503460f94acb93c/html5/thumbnails/16.jpg)
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?
![Page 17: Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2 2. Find the vertex of y = -2x 2 – 8x – 10. 3. Find](https://reader036.vdocuments.net/reader036/viewer/2022062421/56649dd45503460f94acb93c/html5/thumbnails/17.jpg)
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
![Page 18: Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2 2. Find the vertex of y = -2x 2 – 8x – 10. 3. Find](https://reader036.vdocuments.net/reader036/viewer/2022062421/56649dd45503460f94acb93c/html5/thumbnails/18.jpg)
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?
![Page 19: Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2 2. Find the vertex of y = -2x 2 – 8x – 10. 3. Find](https://reader036.vdocuments.net/reader036/viewer/2022062421/56649dd45503460f94acb93c/html5/thumbnails/19.jpg)
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?
![Page 20: Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2 2. Find the vertex of y = -2x 2 – 8x – 10. 3. Find](https://reader036.vdocuments.net/reader036/viewer/2022062421/56649dd45503460f94acb93c/html5/thumbnails/20.jpg)
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?
![Page 21: Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2 2. Find the vertex of y = -2x 2 – 8x – 10. 3. Find](https://reader036.vdocuments.net/reader036/viewer/2022062421/56649dd45503460f94acb93c/html5/thumbnails/21.jpg)
To find the initial height…Find the y-intercept!
![Page 22: Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2 2. Find the vertex of y = -2x 2 – 8x – 10. 3. Find](https://reader036.vdocuments.net/reader036/viewer/2022062421/56649dd45503460f94acb93c/html5/thumbnails/22.jpg)
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?
![Page 23: Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2 2. Find the vertex of y = -2x 2 – 8x – 10. 3. Find](https://reader036.vdocuments.net/reader036/viewer/2022062421/56649dd45503460f94acb93c/html5/thumbnails/23.jpg)
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?
![Page 24: Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2 2. Find the vertex of y = -2x 2 – 8x – 10. 3. Find](https://reader036.vdocuments.net/reader036/viewer/2022062421/56649dd45503460f94acb93c/html5/thumbnails/24.jpg)
Summarize