Warm-up Problems
18
1. Simplify
7
2. Solve -2(x – 3)2 = 24
3. Find the absolute value of 4 – 2i.
3i
4. Write
in standard form.
5  2i
5. Write y = 2x2 – 4x + 15 in vertex form.
6. Solve x2 – 8x = 10
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
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.
h  t   16t 2  32t  4
c) What maximum height do the keys reach and when
do they reach this height?
h  t   16t 2  32t  4
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?
h  t   16t 2  32t  4
e) When do the keys hit the ground?
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.
h  t   16t 2  24t  6
c) What is the height of the ball 1 second after it is
thrown?
h  t   16t 2  24t  6
d) If Hamish doesn’t catch the ball, when does it hit the
ground?
h  t   16t 2  24t  6
e) When does the ball reach the maximum height and
what is this height?
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.
h  t   16t 2  48t  3
c) When does the ball reach the maximum height and
what is this height?
h  t   16t 2  48t  3
d) When does the ball hit the ground?
h  t   16t 2  48t  3
e) When is the softball 12 feet above the ground?