Math Practice Assignment

Question

satellite73 · Answer

sounds annoying...

diamondanon2 · Answer

Sorry lol here

diamondanon2 · Answer

I don't even know where to begin.

marcelie · Answer

is this precal ?

diamondanon2 · Answer

yes

satellite73 · Answer

yikes
first off a cable does not hang as a parabola, but no matter, i guess you can pretend it does

satellite73 · Answer

if the center of the roadway is the origin (like it tells you) then the vertex is 10 feet above that, so $(0,10)$ would be the vertex

diamondanon2 · Answer

oh okay

satellite73 · Answer

i have no idea how you are supposed find the directrix, but perhaps since the vertex is at $(0,10)$ they are imagining the road is the directrix?  do the directrix is $y=0$ but i would not bet more than $7 on that answer

diamondanon2 · Answer

okay

satellite73 · Answer

if that is the case, then the directrix is $(0,20)$

diamondanon2 · Answer

Oh I see

satellite73 · Answer

wait maybe since i am making this up, we should try something else that might work

satellite73 · Answer

we have the vertex at $(0,10)$ for sure, that we can be certain of

diamondanon2 · Answer

sure haha

satellite73 · Answer

we also know that the road is 600 feet, and at the end it is 100 feet high 
if we use the center of the road as the origin, that means we have two other points on the parabola that we know $$(-300,100)$$ and $$(300,100)$$

satellite73 · Answer

so know we can find out what the equation of the parabola is from those two pieces of information

satellite73 · Answer

three pieces actually

satellite73 · Answer

vertex form would be $$y=a(x-h)^2+k$$ we know $h=0,k=10$ so it is 
$$y=ax^2+10$$ 
all we need is $a$

satellite73 · Answer

let me know if i lost you yet

satellite73 · Answer

works out nicely if you solve $$100=a(300)^2+10$$ you get $a=0.001$

diamondanon2 · Answer

oh okay

satellite73 · Answer

that makes your equation 
$$y=.001x^2+10$$ or if you prefer $$y=\frac{1}{1000}x^2+10$$

diamondanon2 · Answer

so now we input a?

satellite73 · Answer

lets back up a sec

satellite73 · Answer

you got a parabola with three known points, 
$(-300,100),(0,10),(300,100)$ where the middle point is the vertex

satellite73 · Answer

that means the equation has to be $$y=ax^2+10$$ and to find $a$ put $y=100,x=300$ and solve for $a$ $$100=a(300)^2+10$$

satellite73 · Answer

when you solve that equation for $a$ you get $$100=9000a+10\
90=9000a\
.001=a$$

satellite73 · Answer

i made a typo there, should be $$100=90000a+10$$ but the solution is right 
now we can find all the other stuff if you like

diamondanon2 · Answer

@satellite73 so in standard form it would be

diamondanon2 · Answer

90000a + 10 = 100

diamondanon2 · Answer

I still need the focus, Latus Rectum, Domain, and Range

diamondanon2 · Answer

and the equation in standard form

diamondanon2 · Answer

I just do not know how :(

diamondanon2 · Answer

@sweetburger

phi · Answer

satellite posted the equation in standard form $$ y=\frac{1}{1000}x^2+10 $$ see http://www.mathwarehouse.com/geometry/parabola/standard-and-vertex-form.php interesting to note that is is *also* in vertex form (the vertex is at (0,10) ) what else do you need ?