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Math Assignment Unit 3 | Complete Mathematics Solutions and Step-by-Step Answers | Study Guide 2026/2027

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Math Assignment Unit 3 | Complete Mathematics Solutions and Step-by-Step Answers | Study Guide 2026/2027

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PA

Math Assignment Unit 3

Data Structures

College Algebra

Math 1201

1st December, 2025

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, Math10/13/2026,
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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:

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