An object is dropped from a height of 60 m. Its height above the ground, h, in meters, is related to the time t, in seconds, since the beginning of its fall by the formula h = - 4.9t ^ 2 + 60.

a)What is the degree of this function

b)What are the dominant coefficient and the constant term of this function What does the constant term represent?

c) What are the restrictions on the field of the function? Explain your choice of restrictions.

d) Describe the infinite behavior of the graph of this function

a) 2

b) dominant coefficient = -4.9, constant term = 60, constant term is the y-intercept

c) domain = R, range = (-∞, 60]

d) goes to minus infinity

Step-by-step explanation

We are given a function h(t) = -4.9t² + 60

a) The degree of a polynomial function is the value of the highest power in the polynomial. We see that since there's t², which is the 2nd power, it means that the degree of this function is 2.

b) The dominant coefficient (also called the leading coefficient) is the coefficient of the term with the highest power. In our function it is the coefficient of the t² term, which is -4.9

The constant term is the coefficient which does not have any variable (t or powers of t) multiplied to it. In our example the constant term is 60

Constant term represents the value of the function when the variable is zero. In other words, it represents the y-intercept.

c) There's no restrictions in the domain for this function (However, in real life time starts from zero)
As for the range, since -4.9t² function always subtracts from 60, then the function's value will be always less than or equal to 60, thus range is (-∞, 60]

d) As t goes to infinity, h(t) will also go to minus infinity. (However, in real life, once h is equal to zero, the object hits the ground and the motion, hence the function, is stopped there)