diver jumps into a pool from a board ten feet above the surface of the water. Her height, h, at any time t seconds after jumping is given by the equation

Question

. What is the minimum height that she reaches? (Note: Negative values of h mean the diver is below the water.)

A.
–26 feet

B.
–10 feet

C.
–6 feet

D.
–4 feet

Answer 1

To determine the minimum height the diver reaches, we need to know the equation that describes her height \( h \) as a function of time \( t \). Since you didn't provide the equation, I can guide you through the general approach to finding the minimum height:

1. Identify the equation: Typically, the height \( h(t) \) can be expressed as a quadratic equation of the form: \[ h(t) = -at^2 + bt + c \] where \( a \), \( b \), and \( c \) are constants.

2. Find the vertex: The minimum (or maximum in this case since it is a downward-opening parabola) height occurs at the vertex of the parabola. The time at which the vertex occurs can be found using the formula: \[ t_{vertex} = -\frac{b}{2a} \]

3. Substitute to find minimum height: Once you find \( t_{vertex} \), substitute it back into the height equation to find the height at that time.

4. Analyse the results: If the calculated height is negative, it indicates how far below the water surface she dips.

Now, if you have the specific equation for height \( h(t) \), you could provide it, and I could assist you further in calculating the minimum height. Based on your options A through D, the results will reflect the different possible minimum heights found from plugging in \( t_{vertex} \) into the height equation.