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anonymous
 one year ago
A building has an entry the shape of a parabolic arch 96 ft high and 18 ft 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 ninety six feet and its width from left to right is eighteen feet.
Find an equation for the parabola if the vertex is put at the origin of the coordinate system.
anonymous
 one year ago
A building has an entry the shape of a parabolic arch 96 ft high and 18 ft 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 ninety six feet and its width from left to right is eighteen feet. Find an equation for the parabola if the vertex is put at the origin of the coordinate system.

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mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0dw:1436844571604:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0\(y = ax^2 + bx + c\) Use each of the three points in the equation above to come up with three equations. Then solve the equations simultaneously for a, b, and c.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how do i use that formula u gave me?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0because its at the origin, and its pointing down, the y would be the height

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0\(0 = a\cdot 0^2 + b \cdot 0 + c\) c = 0

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0That was for point (0, 0). We have c = 0.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So y = 96, since it's axis of symmetry is the origin, the x's on either side would be 9 and 9 SO we have now two points on the parabola. (9,96) and (9,96)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0(96 = a*9^2 + b*9 + 0) (96 = a*9^2 + b*9 + 0) these would be the two equations?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0Now let's try the point (9, 96) \(y = ax^2 + bx\) There is no c bec we already know c is zero. \(96 = a(9^2) + b(9) \) \(81a + 9b = 96\) Here is one equation.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.02 equations? there will be only one equation

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0Now we use the point (9, 96) to get the other equation. \(96 = a(9)^2 + b(9) \) \(96 = 81a  9b\) \(81a  9b = 96\) Here is the other equation. Since now we only have the two variables a and b, all we need is 2 equations. We can now find a and b. We need to solve the system of equations below: \(81a + 9b = 96\) \(81a  9b = 96\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The vertex form, as you probably know, is: y = a(x  h)^2 + k where (h, k) is the vertex and that is point (0, 0), so your equation becomes: y = a(x  0)^2 + 0 or y = ax^2 to find "a", you have to realize that (9, 96) is a point, so: 96 = a(9^2) = 81a a = 96/81 = 32/27 so, y = (32/27)x^2 vertex form: y = (32/27)(x  0)^2 + 0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0from there you can just expand the vertex form to get the standard form

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0Add the equations to eliminate b: \(162a = 192\) \(a = \dfrac{192}{162} = \dfrac{32}{27} \) Now we need b.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I have no idea what math student is doing, we do not need2 equations!!!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok can i get run by this step by step because im so lost

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0using vertex form first then expanding to get standard form is quite simple. Follow my previous long post

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The vertex form, as you probably know, is: y = a(x  h)^2 + k where (h, k) is the vertex and that is point (0, 0), so your equation becomes: y = a(x  0)^2 + 0 or y = ax^2 to find "a", you have to realize that (9, 96) is a point, so: 96 = a(9^2) = 81a a = 96/81 = 32/27 so, y = (32/27)x^2 vertex form: y = (32/27)(x  0)^2 + 0 Then multiply it out to get the standard form.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0OH i now see what math student is doing. Albeit a bit lengthy, but works

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0\(81a + 9b = 96\) \(81\left( \dfrac{32}{27} \right) + 9b = 96\) \(2592 + 243b = 2592\) \(243b = 0\) \(b = 0\) Now we can write the equation of the parabola as: \(y = ax^2 + bx + c\) \(y = \dfrac{32}{27}x^2 \)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so from y = (32/27)(x  0)^2 + 0 the standard form would be y = (32/27)x^2?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Essentially the same thing, but using vertex method then expanding takes fewer time (just a hint for next time)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so that would be my equation for the parabola if the vertex is put at the origin of the coordinate system?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes, that is what we both got.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0perfect thank you very much
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