PA
Math Assignment Unit 3
Data Structures
College Algebra
Math 1201
1st December, 2025
, Task 1: Quadratic Functions (Bungee Jumper) PA
Given: The height of the jumper is modeled by the function:
h(t) = −0.5t² + v₀t + h₀
Where:
● v₀ = 0 m/sec (initial velocity)
● h₀ = 210 meters (initial height)
Substituting these values, the specific function for this scenario is:
h(t) = -0.5t² + 210
(i) Mathematical Understanding
(a) Domain and Range
● Domain: The domain represents the valid time (t) values for the jump. The time starts at t
= 0 and ends when the jumper hits the water (height h = 0).
Solving for h(t) = 0:
−0.5t² + 210 = 0
0.5t² = 210
t² = 420
t = √420 ≈ 20.49 seconds
Answer: The domain is [0, 20.49]. Physically, this represents the duration of the fall from
the bridge until touching the river.
● Range: The range represents the vertical height (h). The maximum height is the start
point (210 m), and the minimum is the river surface (0 m). Answer: The range is [0, 210].
Physically, this represents the vertical space in which the jump occurs.
(b) Vertex of the Function For a quadratic function ax² + bx + c, the t-coordinate of the vertex is
found at t = −b / 2a. Here, a = −0.5 and b = 0.
t = −(−0.5) = 0
Substitute t = 0 into the equation to find h:
h(0) = −0.5(0)² + 210 = 210
Math Assignment Unit 3
Data Structures
College Algebra
Math 1201
1st December, 2025
, Task 1: Quadratic Functions (Bungee Jumper) PA
Given: The height of the jumper is modeled by the function:
h(t) = −0.5t² + v₀t + h₀
Where:
● v₀ = 0 m/sec (initial velocity)
● h₀ = 210 meters (initial height)
Substituting these values, the specific function for this scenario is:
h(t) = -0.5t² + 210
(i) Mathematical Understanding
(a) Domain and Range
● Domain: The domain represents the valid time (t) values for the jump. The time starts at t
= 0 and ends when the jumper hits the water (height h = 0).
Solving for h(t) = 0:
−0.5t² + 210 = 0
0.5t² = 210
t² = 420
t = √420 ≈ 20.49 seconds
Answer: The domain is [0, 20.49]. Physically, this represents the duration of the fall from
the bridge until touching the river.
● Range: The range represents the vertical height (h). The maximum height is the start
point (210 m), and the minimum is the river surface (0 m). Answer: The range is [0, 210].
Physically, this represents the vertical space in which the jump occurs.
(b) Vertex of the Function For a quadratic function ax² + bx + c, the t-coordinate of the vertex is
found at t = −b / 2a. Here, a = −0.5 and b = 0.
t = −(−0.5) = 0
Substitute t = 0 into the equation to find h:
h(0) = −0.5(0)² + 210 = 210
