The vertical height , in feet, of a snowboarder jumping off of an overhang can be modeled by the function h(t)=15-10t-16t^2, where 15 is the initial height (in feet) of the overhang, -10 is the initial vertical velocity (in feet per second), and t is the time (in seconds).
A. how long does it take the snowboarder to land after jumping off the overhang?

Question

The vertical height , in feet, of a snowboarder jumping off of an overhang can be modeled by the function h(t)=15-10t-16t^2, where 15 is the initial height (in feet) of the overhang, -10 is the initial vertical velocity (in feet per second), and t is the time (in seconds).
          A. how long does it take the snowboarder to land after jumping off the overhang?

jdoe0001 · Answer

have you covered quadratics yet?   as in finding the solutions or roots of a quadratic equation?

anonymous · Answer

yeah but I don't remember what we have to do

jdoe0001 · Answer

well... let us notice that the equation given is a parabola firstly

anonymous · Answer

okayyyyy so what does that mean we have to do with a parabola?

jdoe0001 · Answer

yes

and that the leading term coefficient $\bf h(t)=15-10t-16t^2\implies h(t)={\color{brown}{ -16}}t^2-10t+15$  is a negative value

that means first off.    if we set the height over the y-axis and the time over the x-axis

that gives us a vertical parabola
the negative leading coefficient, means the parabola opens downward

so |dw:1407711250943:dw|   so... as you can see, if you solve the equation for "t", that will give you the x-intercepts or "roots" of the quadratic equation, and one of those is how long it took for the snowboarder to land after the jump