This has nothing to do with geometry
[quote=lilmama-14;60314]At time=0, a diver jumps from a diving board that is 32 feet above the water. the hieght of the diver is given by the equation,
h(t)=-16t (squared) +16t+32, where h is measured in feet and t is measured in seconds.
A)when does the diver hit the water?
he hits the water when his height above the water is zero.
solve for h(t) = 0
the domain of a function is the set of all inputs (in this case, t-values) for which the function is defined. technically, the domain of this function is all real t, since it is a polynomial. but generally we don't accept negative values for time, so i'd say dom(h) =B)what is the domain of the equation for height?
the range is the set of all outputs (in this case, h-values) for which the function is defined. the function given is a parabola with a maximum value. find this maximum value. the range will be everything from that value down to -infinity
C)what is the range of the equation for the hieght?
i'm tempted to just blurt out 32 , since the diver was at 32 feet and is diving downwards(but that is likely to be wrong, since it's possible his height increased before it started to decrease), but let's be methodical about this.
D)what is the maximum height reached by the diver?
the maximum height occurs at the vertex. to find the t that gives the vertex, we use the vertex formula: , where the original equation is of the form:
after finding the t-value in this way, plug it into h to solve for the max height