MBF 3CI
Name: _____________________
INTERPRETING GRAPHS OF QUADRATIC EQUATIONS
1. For each parabola below, identify the following information.
a)
3.
Identify the coordinates of the vertex for each parabola.
a) y  3( x  6) 2  1
b) y  4( x  5) 2  10
c) y  8( x  15) 2  12
b)
vertex: ____________
vertex: ____________
vertex: ____________
4. A pebble is fired from a sling shot from the top of a small
hill. The path of the pebble can be modelled by the parabola
h  5.25(t  4) 2  96 where h is the height of the pebble
in metres and t is the time in seconds after the pebble was
fired.
a) Identify the coordinates of the vertex.
x-intercepts:
_________
x-intercepts:
_________
y-intercept:
_________
y-intercept:
_________
vertex:
_________
vertex:
_________
max or min?
_________
max or min?
_________
optimal value: _________
optimal value: _________
(max/min value)
(max/min value)
2. Match each relation with its graph.
b) How long will it take the pebble to reach its maximum
height?
c) What is the maximum height?
a) y  0.5( x  3) 2  2
b) y  2( x  3) 2  2
c) y  ( x  4) 2  1
d) What is the height of the small hill?
5. For each parabola below, identify the following information.
a)
b)
7.
A golf ball is hit from the top of a cliff and fell to the green located
at the bottom of the valley. The path of the golf ball can be
modelled by the parabola h  2.5(t  5) 2  170 where h is the
height in metres above the valley and t is the time after the ball was
hit, in seconds.
a) Identify the coordinates of the vertex.
b) What is the maximum height of the golf ball?
x-intercepts:
_________
x-intercepts:
_________
vertex:
_________
y-intercept:
_________
max/min
_________
vertex:
_________
optimal value:
_________
max/min
_________
optimal value:
_________
c) How long does it take the golf ball to reach its maximum height?
d) What is the height of the ball after 3 s?
e) What is the height of the ball after 7 s?
6. Match each relation with its graph.
f) What do you notice about your answers to parts c) and d)?
a) y  2( x  1) 2  4
g) What is the height of the cliff?
b) y  ( x  1) 2  4
c) y  0.5( x  1) 2  4
8. For each quadratic relation,
i) Determine if the parabola opens up or down
ii) Determine if the parabola is stretched or compressed
iii) Determine the vertex of the parabola
a) y  5( x  2)2  3
b) y  0.25( x  2)2  7
c) y  7 x 2  1
d) y  0.6( x  8)2