6.7.35
1 answer:
Answer:
Step-by-step explanation:
This is most easily solved with calculus, believe it or not. It is way more direct and to the point, with a whole lot less math!
The position function is given. The velocity function is the first derivative of the position, so if we find the velocity function and set it equal to 0, we can solve for the amount of time it takes for the rocket to reach its max height. Remember from physics that at the top of a parabolic path, the velocity is 0.
If:
, then the velocity function, the first derivative is:
v(t) = -32t + 112 and solve for t:
-112 = -32t so
t = 3.5 seconds. Now we know how long it takes to get to the max height, we just need to find out what the max height is.
Go back to the position function and sub in 3.5 for t to tell us that position of the rocket at 3.5 seconds, which translates to the max height:
and
s(3.5) = 206 feet. I imagine that your answer, if you had to choose one from the list, would be 200 feet, rounded a lot.
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Given the vertex, (2, -4) as the minimum point, and that it is an upward-facing parabola that passes point (1, -2):
We could substitute these values into the vertex form of the quadratic function,
f(x) = a(x - h)^2 + k
where:
(h,k) is the vertex
The axis of symmetry is the vertical line x = 2
The value of “a” determines whether the graph opens up or down, and makes the parent function wider or narrower.
The value of “h” determines how far left or right the parent function is translated.
The value of “k” determines how far up or down the parent function is translated.
Now that we’ve established these definitions, we can substitute the given values into the vertex form:
f(x) = a(x - 2)^2 - 4
In order to determine the value of “a”, we must substitute the values of the other given point, (1, -2) into the equation:
f(x) = a(x - 2)^2 - 4
-2 = a(1 - 2)^2 - 4
-2 = a(-1)^2 - 4
-2 = a - 4
Add 4 to both sides to solve for “a”
-2 + 4 = a - 4 + 4
2 = a
Now that we have the value of a = 2, we can establish our quadratic function in vertex form:
f(x) = 2(x - 2)^2 - 4
I’m also including a screenshot of the graph of the function we came up with.
Please mark my answers as the Brainliest if you find my explanations helpful :)
We could substitute these values into the vertex form of the quadratic function,
f(x) = a(x - h)^2 + k
where:
(h,k) is the vertex
The axis of symmetry is the vertical line x = 2
The value of “a” determines whether the graph opens up or down, and makes the parent function wider or narrower.
The value of “h” determines how far left or right the parent function is translated.
The value of “k” determines how far up or down the parent function is translated.
Now that we’ve established these definitions, we can substitute the given values into the vertex form:
f(x) = a(x - 2)^2 - 4
In order to determine the value of “a”, we must substitute the values of the other given point, (1, -2) into the equation:
f(x) = a(x - 2)^2 - 4
-2 = a(1 - 2)^2 - 4
-2 = a(-1)^2 - 4
-2 = a - 4
Add 4 to both sides to solve for “a”
-2 + 4 = a - 4 + 4
2 = a
Now that we have the value of a = 2, we can establish our quadratic function in vertex form:
f(x) = 2(x - 2)^2 - 4
I’m also including a screenshot of the graph of the function we came up with.
Please mark my answers as the Brainliest if you find my explanations helpful :)