World 2-6 Word Problems Involving the Vertex of a Parabola
Name:
Eg. 1. Determine the equation of the parabola in standard form given the coordinates of the vertex and a
point.
a) V(3,6) and P(7,2)
b) V(-1,12) and P(2,-15)
Eg. 2 Bruce is kicking a field goal from 30 m away at a goal post 3 m tall. The ball reaches a maximum
height of 20 m after 18 seconds. Also, the ball is 12 m high after 10 seconds of being in the air.
Eg. 3 Chippy, the beaver is diving into the water to her dam. She enters the water 1s after jumping and gets
to the dam after 5 s. How high is the ledge if she reaches a maximum depth of 6 m below the water?
World 2-6 Word Problems Involving the Vertex of a Parabola
Name:
1. Determine the equation of the parabola with vertex V and passing through a point.
a) V(-1,4) and P(2,-2)
b) V( 0,0) P(-1,2)
c) V(2,0) and P(1,4)
d) V(3,16) and (0,7)
2. Determine the maximum or the minimum of the parabola
2
a) f(x) = -2x +12x -19
2
b) g(x) = 5x – 20x + 4
World 2-6 Word Problems Involving the Vertex of a Parabola
Name:
1. Noah is joining the pro-golfer circuit. He hits a golf ball into the air. It reaches a max height of 122.5 m
after 3.5 seconds and lands at point (7,0).
a) What is the equation of the projectile?
b) How high was the ball after 3 seconds?
c) At 113.5 m, how long was the ball in the air?
2. Isabella loves soccer. She kicks a soccer ball into the air. Using the rule
is the distance and y is the height of the ball in meters.
y = −2 x 2 + 2 x + 10 , where x
a) What is the max height of the ball?
b) How far did the ball travel in the air when it reaches the ground?
3. Eric throws a pig into the air, to see if they really do fly. It follows a trajectory based on the function
f ( x) = − x 2 + 5 x − 6
a) How long was the pig in the air?
b) What was the height of the pig after 3 seconds?
World 2-6 Word Problems Involving the Vertex of a Parabola
Name:
4. Patrick and Cassandra run a baseball experiment and throw a baseball towards a target 4 meters off the
2
ground. The rule associated with the baseball’s flight path is f ( x) = −0.2( x − 6) + 4.21. The
horizontal distance between them and the target is 4.5m. At the moment they throw the ball, what is the
distance between the ball and the ground?
5. For a dance routine Maxine, flies through the air (being attached by a rope from above). She travels a
distance of 10m and reaches a max height of 15m. What rule corresponds to her path?
6. Sarah throws a ball towards a wall. At the moment she throws the ball, it is 1.75m off the ground. The
ball reaches a max height of 8m. On it’s way down, it hits the wall 3m above the ground. The rule of the
ball’s trajectory is
y = −0.25( x − 5) 2 + 8 .
What is the horizontal distance between Sarah and the wall?