1. Warm-up Problems Simplify Solve -2(x – 3)2 = 24
Find the absolute value of 4 – 2i.
Write in standard form.
Write y = 2x2 – 4x + 15 in vertex form.
Solve x2 – 8x = 10

2. 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 ground
t is time
v0 is the initial velocity
h0 is the initial height 2 2 2 2

3. 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.

4. c) What maximum height do the keys reach and when do they reach this height?

5. d) Her brother Mark is standing on a balcony above her
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?

6. e) When do the keys hit the ground?

7. 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.

8. c) What is the height of the ball 1 second after it is thrown?

9. d) If Hamish doesn’t catch the ball, when does it hit the ground?

10. e) When does the ball reach the maximum height and what is this height?

11. 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.

12. c) When does the ball reach the maximum height and what is this height?

13. d) When does the ball hit the ground?

14. e) When is the softball 12 feet above the ground?