Mathematics, 04.11.2019 14:31 kalibaby

Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, -7).

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Answer from: debbie4755

The standard form of the equation of a parabola gives details of the vertex and focus coordinates

The standard form of the equation of the parabola is x² = -28·y

The reason why the equation is correct is given as follows;

The known parameters of the parabola are;

The location of the vertex = The origin, (0, 0)

The location of the focus of the parabola = (0, -7)

Solution:

The equation of the parabola can be expressed as follows;

(x - h)² = 4·p·(y - k)

Where;

(h, k) = The coordinates of the vertex

(h, k + p) = The coordinates of the focus

By comparison with the given coordinates, we have;

(h, k) =The vertex = (0, 0)

h = 0, k = 0

(h, k + p) = The coordinates of the focus = (0, -7)

k + p = -7

0 + p = -7

p = -7

The standard form of the equation of the parabola is therefore;

(x - 0)² = 4 × (-7) × (y - 0)

x² = -28·y

Learn more about the equation of a parabola here:

link

Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0

Answer from: elijaahstepp041

So hmm check the picture below

we know the vertex is at the origin, and the focus point is below it, that means two things, the parabola is vertical and it's opening downwards

notice the distance "p", from the vertex to the focus point, is just 7 units, however, since the parabola is opening downwards, the "p" value will be negative, so p = -7

$\bf \textit{parabola vertex form with focus point distance}\\\\
\begin{array}{llll}
(y-{{ k}})^2=4{{ p}}(x-{{ h}}) \\\\
\boxed{4{{ p}}(y-{{ k}})=(x-{{ h}})^2 }\\
\end{array}
\qquad 
\begin{array}{llll}
vertex\ ({{ h}},{{ k}})\\\\
{{ p}}=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}
\end{array}\\\\
-------------------------------\\\\
4{{ p}}(y-{{ k}})=(x-{{ h}})^2\quad 
\begin{cases}
h=0\\
k=0\\
p=-7
\end{cases}\implies 4(-7)(y-0)=(x-0)^2
\\\\\\
-28y=x^2\implies y=-\cfrac{1}{28}x^2$

Answer from: Quest

answer: given that the roller coaster can accommodate 1600 riders per hour, thus the roller coaster can accomodate 1600 / 60 = 26.67 riders per minute.

given that there are 345 people in the line, the number of minutes it will take for the 345 persons to get into the roller coaster is given by 345 / 26.67 = 12.94 minutes.

therefore, it will take you 12.94 minutes to get to the front of the line.

step-by-step explanation:

Answer from: Quest

christopher is 272,195 year old

step-by-step explanation:

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