SOLUTION: A drone takes off from a platform. Its height h(t), in meters, t seconds after the takeoff can be modeled by the equation h(t) = −t² + 16t + 80. Write the appropriate domain f

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Question 1205890: A drone takes off from a platform. Its height h(t), in meters, t seconds after
the takeoff can be modeled by the equation h(t) = −t² + 16t + 80.
Write the appropriate domain for this function based on the context. For
each box, select the letter before the correct value.
≤t ≤
Ⓐ - 20 Ⓔ - 4
Ⓑ - 4 Ⓕ 0
Ⓒ 0 Ⓖ 4
Ⓓ 4 Ⓗ 20
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

The goal is to find the values of t which make h(t) = 0 true.

You can factor using trial and error, or use the quadratic formula.
I'll use the quadratic formula.

Plug in a = -1, b = 16, c = 80
t+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29

t+=+%28-16%2B-sqrt%28%2816%29%5E2-4%28-1%29%2880%29%29%29%2F%282%28-1%29%29

t+=+%28-16%2B-sqrt%28256+%2B+320%29%29%2F%28-2%29

t+=+%28-16%2B-sqrt%28576%29%29%2F%28-2%29

t+=+%28-16%2B-++24%29%2F%28-2%29

t+=+%28-16%2B24%29%2F%28-2%29 or t+=+%28-16-24%29%2F%28-2%29

t+=+%288%29%2F%28-2%29 or t+=+%28-40%29%2F%28-2%29

t+=+-4 or t+=+20

If t = -4 or t = 20, then h(t) = 0.
I'll let the student confirm this.

The leading coefficient being negative (a = -1) tells us that the parabola opens downward. Therefore, the portion of the curve above the x axis spans from t = -4 to t = 20
h(t) > 0 on the interval -4 < t < 20

h%28t%29+%3E=+0 on the interval -4+%3C=+t+%3C=+20

However, since t is a time value, it makes no sense to have t be negative.
So we must require that t+%3E=+0 as well.

Overlap t+%3E=+0 and -4+%3C=+t+%3C=+20 together to find the final answer is 0+%3C=+t+%3C=+20

Answer by ikleyn(52769) About Me  (Show Source):
You can put this solution on YOUR website!
.

Generally speaking, in mathematical problem books it is not customary
to ask students to solve problems based on a context.
Because who knows what is inside of the author’s head . . .

Yes, sometime students are forced do it, when the author is not able
to present the context explicitly using his own words - - - or is not able
to do it properly; or do not want to make necessary efforts . . .

But this is usually considered as a bad accident and DEFINITELY is NOT a good practice.

In any case, it does not speak well about the authors of such problems, when they
ask students solve a problem based on a context.

When a reader sees such invitation from the author to solve a Math problem based on a context,
a reader (and all people around) may think whether the author needs health procedures to improve his brain . . .