Question

The function h(t) = −5t2 + 15t shown in the graph models the supporting structure of a bridge:

graph of parabola starting at zero comma zero, rising from the left to about one and one half comma 11, and falling to the right, ending at 3 comma zero

What is the domain of h(t)?

a
All real numbers

b
0 ≤ x ≤ 11

c
0 ≤ x ≤ 3

d
x ≥ 0

Answer 1

c) 0 ≤ x ≤ 3.

Explanation:

To determine the domain of the function h(t) = -5t^2 + 15t, we need to identify the values of t for which the function is defined.

Looking at the graph description, we can see that the parabola starts at (0, 0) and ends at (3, 0). This means that the bridge is supported from t = 0 to t = 3.

Therefore, the domain of h(t) is from t = 0 to t = 3, or in interval notation: 0 ≤ t ≤ 3.

However, in the given answer options, the variable is referred to as x instead of t. Therefore, the correct option would be:

c) 0 ≤ x ≤ 3.

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