The required equation of the parabola is (y-5)² = 20(x+2)
<h3>Equation of a parabola</h3>
The standard equation of a parabola is expressed as;
(y-k)² = 4p(x-h)
where;
vertex = (h, k)
focus = (p+k, k)
directrix x = -p + h
Note that the directrix given will determine the type of the equation of a parabola
Given the following parameters
focus = (-2, 5) = (h, k)
x = -p + h
3 = p -2
p = 5
Substitute
(y-k)² = 4p(x-h)
(y-5)² = 4(5)(x-(-2))
(y-5)² = 20(x+2)
Hence the required equation of the parabola is (y-5)² = 20(x+2)
Learn more on equation of parabola here; brainly.com/question/4061870
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Answer:
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Step-by-step explanation:
y-7=4(x-2)
we need to simplify the y to het a
y-7=4x-8 (i did 4x-8 because of 4(x-2)
now y= 4x-8+(-7)
after calculating -8+(-7) IT becomes
y=4x-15
okay we have the guide Line
y=4x-15
the a is 4
because
a = {y=a.x+b}
now we need to find the points using this guide Line
y=4x-15
x= 2(you can add any number here ,we Just need to know where the point is )
y= 4(2)-15
y=8-15
y= -7
points are (2,7)
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.
