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anonymous
 one year ago
MEDAL AND FAN!!!
A tunnel is in the shape of a parabola. The maximum height is 50 m and it is 10 m wide at the base as shown below.
A parabola opening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 50 meters and its width from left to right is 10 meters.
What is the vertical clearance 2 m from the edge of the tunnel?
I will post a picture in a second.
anonymous
 one year ago
MEDAL AND FAN!!! A tunnel is in the shape of a parabola. The maximum height is 50 m and it is 10 m wide at the base as shown below. A parabola opening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 50 meters and its width from left to right is 10 meters. What is the vertical clearance 2 m from the edge of the tunnel? I will post a picture in a second.

This Question is Closed

phi
 one year ago
Best ResponseYou've already chosen the best response.1do you know the equation of a parabola in "vertex form" ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is it (xh)^2? i kind of forget

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0My answer choice are: 18 m 32 m 46 m 4 m I was thinking I could approximate at 32m...

phi
 one year ago
Best ResponseYou've already chosen the best response.1where (h,k) is the vertex (in this case the "top" of the parabola) next do you have a picture ? with any luck you could sketch it. it would look like this dw:1439209730473:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0actually the turning point, or vertex is at the origin

phi
 one year ago
Best ResponseYou've already chosen the best response.1the reason to study math is to practice "thinking". (or "puzzle things out" if you like) we can draw the picture any way we like. if we use my picture, what are the coordinates of the vertex?

phi
 one year ago
Best ResponseYou've already chosen the best response.1if you put those numbers into the equation what do we get ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0y = a(xh)^2 + k y = a(x0)^2 + 50

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0for my problem the equation would simplify to y = a(x)^2 right?

phi
 one year ago
Best ResponseYou've already chosen the best response.1ok and x0 can be simplified to x, so y= ax^2 + 50 next, notice we are told the width (at ground level ) is 10 and with the origin at the middle, one side is at (5,0) put those numbers in for x and y and "solve for a"

phi
 one year ago
Best ResponseYou've already chosen the best response.1**y = a(x)^2 right?*** you mean y= a x^2 + 50

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i was saying for my equation...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0with the parable i am supposed to be working with. just making sure i am understanding.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0also trying to show that i am understanding what you are saying

phi
 one year ago
Best ResponseYou've already chosen the best response.1let's use my picture, then we will go back and use your picture.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0y = ax^2 + 50 0 = a(5)^2 + 50

anonymous
 one year ago
Best ResponseYou've already chosen the best response.00 = 25a + 50 50 = 25a 2 = a

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes, so the equation is y= 2 x^2 + 50 next we have to interpret **vertical clearance 2 m from the edge *** all the way to the edge is 5 meters. if we move 2 m to the left, what x value is that ?

phi
 one year ago
Best ResponseYou've already chosen the best response.1now we use x=3 in the equation and find y. y will be the vertical height

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0y= 2 x^2 + 50 y = 2 (3)^2 + 50 y = 2 (9) + 50 y = 18 + 50 y = 32

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh lol so if this was the parabola in the equation the answer would be 32? I think this is also the same for my parabola because we have the same dimensions. I will check

phi
 one year ago
Best ResponseYou've already chosen the best response.1looks like your guess way up top was a good one. if we draw the parabola with the vertex at (0,0), it looks like this dw:1439210510774:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0please give me a medal @saseal

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes, we will get the same answer. with the origin at the vertex, the equation is y= a x^2 now we put in the point (5,50) and solve for a 50= a*5*5 a= 2 y= 2 x^2

phi
 one year ago
Best ResponseYou've already chosen the best response.1next, we put in x=3 to find y y= 2 *3*3 y= 2*9= 18 now we have to be careful. that is not the height. that is the distance down from the vertex the height above the "bottom" at y= 50 is the difference between 18 and 50
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