Answer:
[tex]\large \boxed{y = -\dfrac{1}{49}x^{2}+ 25}[/tex]
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
[tex]\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 $\large \boxed{\mathbf{y = -\dfrac{1}{49}x^{2}+ 25}}$}[/tex]
The graph below shows the profile of your bridge. It is 25 m high with a 70 m span.
