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

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

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.

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

216 32 4h t t t

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

e) When do the keys hit the ground?

216 32 4h t t t

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.

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

216 24 6h t t t

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

216 24 6h t t t

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

216 24 6h t t t

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.

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

216 48 3h t t t

d) When does the ball hit the ground?

216 48 3h t t t

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

216 48 3h t t t