Question

a grasshopper jumps off of a tree stump. the height, in feet, of the grasshopper above the ground after t seconds is modeled by the function shown. h(t)= -t^2 + 4/3t + 1/4
After how many seconds will the grasshopper land on the ground?

Answer 1

The function h(t)= -t^2 + 4/3t + 1/4 is a quadratic function

The grasshopper lands on the ground after 1.5 seconds

How to determine when the grasshopper lands on the ground?

The function is given as:

h(t)= -t^2 + 4/3t + 1/4

When the grasshopper lands on the ground, h(t) = 0.

So, we have:

-t^2 + 4/3t + 1/4 = 0

Multiply through by -12

12t^2 - 16t - 3 = 0

Expand

12t^2 + 2t - 18t - 3 = 0

Factorize

2t(6t + 1) - 3(6t + 1) = 0

Factor out 6t + 1

(2t- 3)(6t + 1) = 0

Split

2t- 3 = 0 or 6t + 1 = 0

Solve for t

t = 1.5 or t = -1/6

Time cannot be negative.

So:

t = 1.5

Hence, the grasshopper lands on the ground after 1.5 seconds

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