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Warm-up Problems 1.Simplify 2.Solve -2(x – 3) 2 = 24 3.Find the absolute value of 4 – 2i....
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Transcript of Warm-up Problems 1.Simplify 2.Solve -2(x – 3) 2 = 24 3.Find the absolute value of 4 – 2i....
![Page 1: Warm-up Problems 1.Simplify 2.Solve -2(x – 3) 2 = 24 3.Find the absolute value of 4 – 2i. 4.Write in standard form. 5.Write y = 2x 2 – 4x + 15 in vertex.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649d6e5503460f94a4e843/html5/thumbnails/1.jpg)
Warm-up Problems
1. Simplify
2. Solve -2(x – 3)2 = 243. Find the absolute value of 4 – 2i.
4. Write in standard form.
5. Write y = 2x2 – 4x + 15 in vertex form.
6. Solve x2 – 8x = 10
3
5 2
i
i
18
7
![Page 2: Warm-up Problems 1.Simplify 2.Solve -2(x – 3) 2 = 24 3.Find the absolute value of 4 – 2i. 4.Write in standard form. 5.Write y = 2x 2 – 4x + 15 in vertex.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649d6e5503460f94a4e843/html5/thumbnails/2.jpg)
Quadratic Applications
In a motion problem, the height of an object is the function
h(t) = -16t2 + v0t + h0
h(t) is the height above the groundt is timev0 is the initial velocityh0 is the initial height
![Page 3: Warm-up Problems 1.Simplify 2.Solve -2(x – 3) 2 = 24 3.Find the absolute value of 4 – 2i. 4.Write in standard form. 5.Write y = 2x 2 – 4x + 15 in vertex.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649d6e5503460f94a4e843/html5/thumbnails/3.jpg)
1. Shelly throws her keys up in the air, releasing them from a height of 4 ft above the ground, with an initial vertical velocity of 32ft/s.a) Write an equation to model path of her keys.
b) Sketch a graph of the situation.
![Page 4: Warm-up Problems 1.Simplify 2.Solve -2(x – 3) 2 = 24 3.Find the absolute value of 4 – 2i. 4.Write in standard form. 5.Write y = 2x 2 – 4x + 15 in vertex.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649d6e5503460f94a4e843/html5/thumbnails/4.jpg)
c) What maximum height do the keys reach and when do they reach this height?
216 32 4h t t t
![Page 5: Warm-up Problems 1.Simplify 2.Solve -2(x – 3) 2 = 24 3.Find the absolute value of 4 – 2i. 4.Write in standard form. 5.Write y = 2x 2 – 4x + 15 in vertex.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649d6e5503460f94a4e843/html5/thumbnails/5.jpg)
d) Her brother Mark is standing on a balcony above her. If his outstretched arms are 16 ft above the ground, at what time(s) can he catch the keys?
216 32 4h t t t
![Page 6: Warm-up Problems 1.Simplify 2.Solve -2(x – 3) 2 = 24 3.Find the absolute value of 4 – 2i. 4.Write in standard form. 5.Write y = 2x 2 – 4x + 15 in vertex.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649d6e5503460f94a4e843/html5/thumbnails/6.jpg)
e) When do the keys hit the ground?
216 32 4h t t t
![Page 7: Warm-up Problems 1.Simplify 2.Solve -2(x – 3) 2 = 24 3.Find the absolute value of 4 – 2i. 4.Write in standard form. 5.Write y = 2x 2 – 4x + 15 in vertex.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649d6e5503460f94a4e843/html5/thumbnails/7.jpg)
2. Hamish throws a baseball straight up with a velocity of 24 ft/s from an initial height of 6ft.a) Write an equation that describes the height of the ball as a function of time.
b) Sketch a graph of the situation.
![Page 8: Warm-up Problems 1.Simplify 2.Solve -2(x – 3) 2 = 24 3.Find the absolute value of 4 – 2i. 4.Write in standard form. 5.Write y = 2x 2 – 4x + 15 in vertex.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649d6e5503460f94a4e843/html5/thumbnails/8.jpg)
c) What is the height of the ball 1 second after it is thrown?
216 24 6h t t t
![Page 9: Warm-up Problems 1.Simplify 2.Solve -2(x – 3) 2 = 24 3.Find the absolute value of 4 – 2i. 4.Write in standard form. 5.Write y = 2x 2 – 4x + 15 in vertex.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649d6e5503460f94a4e843/html5/thumbnails/9.jpg)
d) If Hamish doesn’t catch the ball, when does it hit the ground?
216 24 6h t t t
![Page 10: Warm-up Problems 1.Simplify 2.Solve -2(x – 3) 2 = 24 3.Find the absolute value of 4 – 2i. 4.Write in standard form. 5.Write y = 2x 2 – 4x + 15 in vertex.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649d6e5503460f94a4e843/html5/thumbnails/10.jpg)
e) When does the ball reach the maximum height and what is this height?
216 24 6h t t t
![Page 11: Warm-up Problems 1.Simplify 2.Solve -2(x – 3) 2 = 24 3.Find the absolute value of 4 – 2i. 4.Write in standard form. 5.Write y = 2x 2 – 4x + 15 in vertex.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649d6e5503460f94a4e843/html5/thumbnails/11.jpg)
3. Carol throws a softball upward from a height of 3 ft about the ground with an initial velocity of 48ft/s.a) Write an equation to model the height of the softball.
b) Sketch a graph of the situation.
![Page 12: Warm-up Problems 1.Simplify 2.Solve -2(x – 3) 2 = 24 3.Find the absolute value of 4 – 2i. 4.Write in standard form. 5.Write y = 2x 2 – 4x + 15 in vertex.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649d6e5503460f94a4e843/html5/thumbnails/12.jpg)
c) When does the ball reach the maximum height and what is this height?
216 48 3h t t t
![Page 13: Warm-up Problems 1.Simplify 2.Solve -2(x – 3) 2 = 24 3.Find the absolute value of 4 – 2i. 4.Write in standard form. 5.Write y = 2x 2 – 4x + 15 in vertex.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649d6e5503460f94a4e843/html5/thumbnails/13.jpg)
d) When does the ball hit the ground?
216 48 3h t t t
![Page 14: Warm-up Problems 1.Simplify 2.Solve -2(x – 3) 2 = 24 3.Find the absolute value of 4 – 2i. 4.Write in standard form. 5.Write y = 2x 2 – 4x + 15 in vertex.](https://reader036.fdocuments.in/reader036/viewer/2022081519/56649d6e5503460f94a4e843/html5/thumbnails/14.jpg)
e) When is the softball 12 feet above the ground?
216 48 3h t t t