The height of a rock thrown from a cliff can be modeled by the function h(t) = -16t^2+156t+ 306, where t is the
time after the rock is thrown, in seconds.

when does the rock reach its maximum height?

what is the maximum height?

when does the rock hit the ground?

Step-by-step explanation:

These questions are more easily answered if the equation is written in vertex form. Subtracting the constant and dividing out -16, we get ...

  h(t) -306 = -16(t^2 -9.75t)

Adding the square of half the t-coefficient inside parentheses gives ...

  h(t) -306 -380.25 = -16(t^2 -9.75t +23.765625)

  h(t) = -16(t -4.875)^2 + 686.25

This tells us the maximum height is 686.25 ft at time t = 4.875 seconds.

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When the rock hits the ground, h(t) = 0, so ...

  0 = -16(t -4.875)^2 + 686.25

  686.25/16 = (t -4.875)^2 . . . . . subtract 686.25, divide by -16

  √42.890625 +4.875 = t ≈ 11.424 . . . . take the square root, add 4.875

The rock hits the ground after about 11.424 seconds.

stew reads at the fastest rate of 265 words per minute.

step-by-step explanation:

it's a given that felicia reads at 260 word per minute and on connie's graph we can see that she reads 200 words per minute. since stew's table tells us that he read 795 in 3 minutes, we can divide 795 by 3 to find out how many words he reads per minute.

795/3 = 265

stew reads 265 words per minute - he reads at the fastest rate since felecia reads at 260 words per minute and connie reads at 200 words per minute.

stew (265) > felecia (260) > connie (200)