Aball is thrown straight up from the top of a building 132 ft. tall with an initial velocity of 48 ft per second. the distance s(t) (in feet) of the ball from the ground is given by s(t) = 132 + 48t − 16t2. find the maximum height attained by the ball.

The line of symmetry through the parabola described by s(t) is

... t = -48/(2×(-16)) = 1.5

This is the time at which the ball reaches its maximum height.

... s(1.5) = 132 + 48×1.5 -16×1.5²

... s(1.5) = 132 + 72 - 36 = 168

The maximum height attained by the ball is 168 ft.

check the picture below.

so the maximum height of the ball is obtained at the vertex's y-coordinate, hmm what is it anyway?

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!

b

step-by-step explanation: