Agrasshopper jumps off a tree stump. the height, in feet, of the grasshopper above the ground after t seconds is modeled by the function shown.
h(t) = -t² + 4/3t + 1/4
after how many seconds will the grasshopper land on the ground?

Hence, Grasshopper will land on the ground after 1.5 sec.

Step-by-step explanation:

It s given that:

The height, in feet, of the grasshopper above the ground after t seconds is modeled by the function:

Now we are asked to find:

In how many seconds will the grasshopper land on the ground?

i.e. we have to find the value of t such that h(t)=0

i.e.

i.e. we need to find the roots of the given quadratic equation.

On solving the quadratic equation or plotting it's graph we could observe that the point where h(t)=0 are:

As time can't be negative hence we will consider:

Hence, grasshopper will land on the ground after 1.5 sec.

A graph of a proportional relationship is a straight line that passes through the origin. The constant of a proportionality in a graph of a proportional relationship is the constant ratio of y to x (the slope of the line).
Hope this may help you❤️