Question

What kind of function is this (linear, quadratic, exponential)? Explain how you know
H(t)=400−16t^2

Answer 1

The function \( H(t) = 400 - 16t^2 \) is a **quadratic function**.

### Explanation:

1. **Definition of Quadratic Function**: A quadratic function is generally expressed in the form \( f(x) = ax^2 + bx + c \), where \( a \), \( b \), and \( c \) are constants, and \( a \) is not equal to zero.

2. **Identifying Structure**: In the given function \( H(t) = 400 - 16t^2 \):
- The term \( -16t^2 \) indicates that this is a quadratic term (since the variable \( t \) is raised to the power of 2).
- The constant term \( 400 \) can be seen as the value of \( c \).
- There is no linear term (the coefficient of \( t \) is 0 since there is no \( t \) term present).

3. **Nature of the Graph**: The graph of a quadratic function is a parabola. Since the coefficient of \( t^2 \) (which is \(-16\)) is negative, this parabola opens downwards.

### Conclusion:
Because of the presence of the \( t^2 \) term and the absence of a \( t \) term, we conclude that \( H(t) = 400 - 16t^2 \) is a quadratic function.