Interpreting Algebraic Models Question 8

h(t)=-16t^2+55t+35

The function above models the height $h$ , in feet, of an object above ground $t$ seconds after being launched straight up in the air. What does the number $35$ represent in the function?

The initial height, in feet, of the object.

The maximum height, in feet, of the object.

The initial speed, in feet per second, of the object.

The maximum speed, in feet per second, of the object.

Approach

Since the model represents the height of the object, we cannot obtain the initial speed or maximum speed directly (unless you know a bit of calculus).

The initial height of the object is given with $h(0)$ .

h(t)=-16t^2+55t+35

h(0)=-16(0)^2+55(0)+35

h(0)=35

The maximum height is given by the maximum value. In the case of downward facing parabolas, we would need to find the $x$ value of the vertex.

x=-\frac{b}{2a}

x=-\frac{55}{2(-16)}

x=\frac{55}{32}