Advanced algebra help!?

Question

I have a word problem question that I am stuck on. Please help me and explain, thanks a lot in advance.

In a factory, a parabolic mirror to be used in a searchlight was placed on the floor. It measured 30cm tall and 60cm wide. Find an equation of the parabola.

Answer 1

The equation of the parabola depends on where u consider the origin and which directions u consider as the co-ordinate axes

Let us assume that the vertex of the parabola is at origin , the horizontal to be the x-axis and vertical to be y-axis

Then the general equation of any such parabola is x^2 = 4ay

now we also know that when we consider y = 30 then it implies that x = 30 ( half of 60 ......u will understand why this is if u draw any general parabola in xy plane )

so the point (30,30) has to satisfy the equation of the parabola

implies 30^2 = 4a * 30 which implies 4a = 30

so the required equation becomes x^2 = 30 y
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Answer 2

Let the equation of the mirror be
y = ax² + bx + c.
and place the left bottom edge of the parabola
at the origin.
Now we know 3 noncollinear points on the curve
so we can find a,b and c.
First, (0,0) is on the curve, so c = 0.
Next, (30, 30) is on the curve, since the
x coordinate of the vertex is halfway between the
two x-intercepts.
So 900a + 30b = 30
30a + b = 1.
Finally, (60,0) is on the curve
so
3600a + 60b = 0
60 a + b = 0.
Subtracting the two equations, we get
-30a = 1
a = -1/30
-2 + b = 0
b = 2
So y = -1/30 x² + 2x
is an equation of the parabola.

Answer 3

The equation for a parabola is

y = a(x - h)^2 + k

h and k are the coordinates of the vertex, which we will assume is 0,0.

y = ax^2

30 = a(30)^2
30 = a(900)
a = 30/900 = 1/30

y = 1/30 * x^2

Answer 4

u have to plug those numbers into the formula of the parabola, wich is pretty difficult for me to type down on computer. u could go to google.com and type in formula for a parabula and it would be easier because numbers will plug in correctly