Quadratic Function Applications
Period
Name
Date
Quadratic Function Applications 1) GRAVITATION
F r o m 4 feet a b o v e a s w i m m i n g pool
S u s a n throws a ball upward w i t h
v e l o c t t y o f 3 2 feet p e r s e c o n d . T h e h e i g h t hit) o f t h e b a l l t s e c o n d s a l t e r S u s a n t h r o w s i is g i v e n b y hit)
=
+ 32« + 4. F i n d t h e m a x i m u m h e i g h t r e a c h e d b y t h e b a l l a n d
t h e t i m e t h a t t h i s h e i g h t i s reacht?d.
2)
TICKETING Tlie manager of a symphony computes that the symphony will earn ™40P- - 1 lOOP dollars per concert i f they charge P dollars for tickets. What ticket price should the syrophony charge i n order to maximize its profits?
3)
A R C H E S A n architect decides to use a parabolic arch for the main entrance of a science museum. In one of his plans, the top edge of the arch is described by the graph of y = - | j c 2 + | x + ^ . What
are the coordinates of the vertex of this parabola?
4)
TRAJECTORIES A cannonball is launched from a cannon at the top of a cliff. If the path of the cannonball is traced on a piece of graph paper aligned so that the cannon is situated on the j - a x i s , the equation that describes the path is
y = ™^x2
+ 1^
+
47,
where x is the horizontal distance from the cliffand V is the vertical distance above the ground in feet. How high above the ground is the cannon?
5) F o r E x e r c i s e s 9 a n d 10, um the f o r m u l a hit} = - 161^, w h e r e hit) o f a n object i n feet, is the object's i n i t i a l v e l o c i t y i n feet per t i m e i n i^econds. 9. B A S E B A L L
is the height s e c o n d , a n d t is
the
Marta t h r o w s a baseball w i t h a n i n i t i a l u p w a r d velocity of 60 feet per second.
I g a o n n g M a r t a ' s height, how long after she releases the ball w i l l it h i t the i p ^ u n d ? 10. V O L C A N O E S A volcanic e r u p t i o n b l a s t s a boulder u p w a r d w i t h a n i n i t i a l velocity
of
240 feet per second. H o w long w i l l i t t a k e the boulder to hit the g r o u n d i f it l a n d s at t h e s a m e elevation from w h i c h i t w a s ejected?
6) T R A J E C T O R I E S D a v i d threw a baseball intf) the air. The function of the height of the baseball i n feet is = 80* - 16^^^ where t represents the time i n seconds after the ball was thrown. Use this graph of the function to determine how long it took for the b a l l to fall back to the ground.
Name
Date
Quadratic Function Applications 1) GRAVITATION
F r o m 4 feet a b o v e a s w i m m i n g pool
S u s a n throws a ball upward w i t h
v e l o c t t y o f 3 2 feet p e r s e c o n d . T h e h e i g h t hit) o f t h e b a l l t s e c o n d s a l t e r S u s a n t h r o w s i is g i v e n b y hit)
=
+ 32« + 4. F i n d t h e m a x i m u m h e i g h t r e a c h e d b y t h e b a l l a n d
t h e t i m e t h a t t h i s h e i g h t i s reacht?d.
2)
TICKETING Tlie manager of a symphony computes that the symphony will earn ™40P- - 1 lOOP dollars per concert i f they charge P dollars for tickets. What ticket price should the syrophony charge i n order to maximize its profits?
3)
A R C H E S A n architect decides to use a parabolic arch for the main entrance of a science museum. In one of his plans, the top edge of the arch is described by the graph of y = - | j c 2 + | x + ^ . What
are the coordinates of the vertex of this parabola?
4)
TRAJECTORIES A cannonball is launched from a cannon at the top of a cliff. If the path of the cannonball is traced on a piece of graph paper aligned so that the cannon is situated on the j - a x i s , the equation that describes the path is
y = ™^x2
+ 1^
+
47,
where x is the horizontal distance from the cliffand V is the vertical distance above the ground in feet. How high above the ground is the cannon?
5) F o r E x e r c i s e s 9 a n d 10, um the f o r m u l a hit} = - 161^, w h e r e hit) o f a n object i n feet, is the object's i n i t i a l v e l o c i t y i n feet per t i m e i n i^econds. 9. B A S E B A L L
is the height s e c o n d , a n d t is
the
Marta t h r o w s a baseball w i t h a n i n i t i a l u p w a r d velocity of 60 feet per second.
I g a o n n g M a r t a ' s height, how long after she releases the ball w i l l it h i t the i p ^ u n d ? 10. V O L C A N O E S A volcanic e r u p t i o n b l a s t s a boulder u p w a r d w i t h a n i n i t i a l velocity
of
240 feet per second. H o w long w i l l i t t a k e the boulder to hit the g r o u n d i f it l a n d s at t h e s a m e elevation from w h i c h i t w a s ejected?
6) T R A J E C T O R I E S D a v i d threw a baseball intf) the air. The function of the height of the baseball i n feet is = 80* - 16^^^ where t represents the time i n seconds after the ball was thrown. Use this graph of the function to determine how long it took for the b a l l to fall back to the ground.
