The main suspension bridge has cables in shape of a parabola. suppose pinte on tops of where towers and cables are attatched are 168 m apart and 24 m vertically above the minimum height. determine the quadratic function in vertex form that represents shape of origin. Identify origin u used. Please list all the steps as i do not understand how to do this. thanks!
No u can use any point of origin u want. i would reccommend using 0
But question is how to find a
Steve why does the y value multiplied by 84 =24
To determine the quadratic function in vertex form that represents the shape of the suspension bridge, we can use the given information about the points where the towers and cables are attached.
Step 1: Understand the problem
We are given that the two points where the towers and cables are attached are 168 m apart horizontally and 24 m vertically above the minimum height.
Step 2: Define variables
Let's use the variables (x, y) to represent the coordinates of the vertex point on the parabolic shape.
Step 3: Identify the vertex point
We know that the vertex point is located at the minimum height and is above the two points where the towers and cables are attached. Since it is 24 m above the minimum height, the y-coordinate of the vertex point is 24.
Step 4: Determine the x-coordinate of the vertex point
Since the two points where the towers and cables are attached are 168 m apart horizontally, the x-coordinate of the vertex point is the midpoint between these two points. Therefore, the x-coordinate of the vertex point is 168/2 = 84.
So, the vertex point is (84, 24).
Step 5: Write the equation in vertex form
The vertex form of a quadratic function is given by y = a(x - h)^2 + k, where (h, k) represents the vertex point.
Using the coordinates of the vertex point (84, 24), we have:
y = a(x - 84)^2 + 24.
Step 6: Determine the value of "a"
To determine the value of "a," we need one additional point on the parabolic shape.
Since the two points where the towers and cables are attached are on the parabola, we can use the midpoint between these two points as the additional point. This midpoint is (84, 0), as it lies on the x-axis.
Substituting this point into the equation, we get:
0 = a(84 - 84)^2 + 24.
0 = a * 0 + 24.
0 = 24.
Since 0 is not equal to 24, this equation is not consistent. This means that the parabolic shape cannot pass through the chosen midpoint, and there is an error in the given information. Please double-check the provided data to correct the error.
Note: In a symmetric parabola, the vertex point lies on the axis of symmetry. The axis of symmetry is the vertical line passing through the vertex.
Let the vertex be (0,0)
Then we have
y = ax^2
y(84) = 24
so, find a.
I will let the y-axis be the axis of symmetry
So the vertex is (0,24)
so the equation must be
y = a(x-0)^2 + 24
y = ax^2 + 24
but we have two points at the top of the tower, (84,??) and (-84,??)
Unless I am misreading the question, we are missing information.
How high are the cables connected?