Question

A bridge spans a horizontal distance of 70m and

Answer 1

Answer:

$\large \boxed{y = -\dfrac{1}{49}x^{2}+ 25}$

Step-by-step explanation:

The vertex form of the equation for a parabola is

y = a(x - h)² + k

where h and k are the coordinates of the vertex

and a is a constant.

Make the y-axis the axis of symmetry.

Data:

Vertex at (0, 25)

x-intercepts at (-35, 0) and (35, 0)

Calculations:

1. Substitute the coordinates of the vertex into the equation

y = a(x - 0)² + 25

y = ax² + 25

2. Substitute the coordinates of an x-intercept into the equation and solve for a

$\begin{array}{rcl}0&=& a(35)^{2} + 25\\0& = & 1225a + 25\\a& = & -\dfrac{25}{1225}\\\\a& = & -\dfrac{1}{49}\\\\\mathbf{a}& = & \mathbf{-\dfrac{1}{49}x^{2}+ 25}\\\\\end{array}\\\text{The equation of the parabola is \large \boxed{\mathbf{y = -\dfrac{1}{49}x^{2}+ 25}} }$

The graph below shows the profile of your bridge. It is 25 m high with a 70 m span.