5.3 Day 2 Golf Problem
5.3 Day 2 Golf Problem
Objective: SOLVE QUADRATICS IN VERTEX FORM.
Mar 8 ­ 1:46 PM
1
5.3 Day 2 Golf Problem
Golf Problem
Russel hits a golf ball, the path of which
can be approximated by the equation:
1
y = ‐ 400
(x ‐ 140) 2 + 49
y = height of the ball, in yards
x = horizontal distance, in yards
Mar 8 ­ 1:46 PM
2
5.3 Day 2 Golf Problem
Part A: Find the height of the ball after it has
traveled a horizontal distance of 100 yards.
Show your work and label your answer.
Mar 8 ­ 1:46 PM
3
5.3 Day 2 Golf Problem
Part B: What do the x‐intercepts represent in
the context of the problem? Write complete
sentences explaining your reasoning.
Mar 8 ­ 1:46 PM
4
5.3 Day 2 Golf Problem
Part C: Study the diagram below. The diagram
shows a tree at a horizontal distance of 160 yards
from the starting point of the ball. The tree is 139
feet tall.
139 feet
160 yards
Drawing NOT to scale.
By how many feet will the ball clear the tree?
Show your work and label your answer.
Mar 8 ­ 1:46 PM
5
5.3 Day 2 Golf Problem
Mar 8 ­ 1:46 PM
6
5.3 Day 2 Golf Problem
Golf Problem
ANSWERS
Russel hits a golf ball, the path of which
can be approximated by the equation: y
1
= ‐ 400 (x ‐ 140) 2 + 49
y = height of the ball, in yards
x = horizontal distance, in yards
Mar 8 ­ 1:46 PM
7
5.3 Day 2 Golf Problem
Part A: Find the height of the ball after it has
traveled a horizontal distance of 100 yards.
Show your work and label your answer.
x = 100
2
1
y = ‐ 400 (x ‐ 140) + 49
1
y = ‐ 400
(100 ‐ 140)2 + 49
y=
1
‐ 400
2
(‐ 40) + 49
1
y = ‐ 400
(1600) + 49
y = ‐ 4 + 49
y = 45 yards
Mar 8 ­ 1:46 PM
8
5.3 Day 2 Golf Problem
Part B: What do the x‐intercepts represent in
the context of the problem? Write complete
sentences explaining your reasoning.
The ball follows the path of an inverted
parabola. In the context of the problem the
ball starts on the ground. It is hit into the air
and comes back down to the ground.
Therefore, the x‐intercepts are the points
where the ball is on the ground.
Mar 8 ­ 1:46 PM
9
5.3 Day 2 Golf Problem
Part C: Study the diagram below. The diagram
shows a tree at a horizontal distance of 160 yards
from the starting point of the ball. The tree is 139
feet tall.
139 feet
160 yards
Drawing NOT to scale.
By how many feet will the ball clear the tree?
Show your work and label your answer.
WORK ON NEXT PAGE
Mar 8 ­ 1:46 PM
10
5.3 Day 2 Golf Problem
139 feet
160 yards
Drawing NOT to scale.
2
1
y = ‐ 400
(x ‐ 140) + 49
y=
y=
y=
1
‐ 400
1
‐ 400
1
‐ 400
y = height of the ball, in yards
x = horizontal distance, in yards
2
(160 ‐ 140) + 49
2
(20) + 49
(400) + 49
y = ‐ 1 + 49
ANSWER MUST BE
CONVERTED TO FT
y = 48 yards
Mar 8 ­ 1:46 PM
11
5.3 Day 2 Golf Problem
139 feet
160 yards
Drawing NOT to scale.
2
1
of the ball, in yards
y = ‐ 400
(x ‐ 140) + 49 xy == height
horizontal distance, in yards
y = 48 yards CHANGE TO FEET
1 yard = 3 feet
48 (3) = 144 feet
144 ‐ 139 = 5 ft
Therefore, the ball clears the tree by 5 feet.
Mar 8 ­ 1:46 PM
12