Observing the grid overlay on the bridge, here are five points that align with the arch's curve, starting from the origin and moving outward symmetrically:

1. $(0, 0)$ - Origin point
2. $(2, 2)$ - Right side of the arch
3. $(4, -2)$ - Right side, closer to the base
4. $(-2, 2)$ - Left side of the arch
5. $(-4, -2)$ - Left side, closer to the base

These points can be used to fit a parabolic equation in the form $y = ax^2 + bx + c$. Let me proceed to calculate the values for $a$, $b$, and $c$ that define this parabola.The parabolic equation that best fits the bridge's arch, based on the points chosen, is:

$y = -\frac{3}{4}x^2 + \frac{5}{2}x$

This equation represents a downward-opening parabola that aligns closely with the arch shape observed in the image.

Would you like a plot of this parabola overlaid on the image, or do you have any questions about the calculation process?

Here are five questions to consider for further exploration:

1. How would the parabola change if we selected different points along the bridge's arch?
2. What role does each coefficient ($a$, $b$, and $c$) play in shaping the parabola?
3. Could we model the arch with a different type of curve, like a sine function?
4. What would the equation look like if the arch were symmetric around a different point?
5. How would we handle fitting if the arch had an irregular shape?

Tip: In parabolic equations, the coefficient of $x^2$ determines the "width" and direction (upward or downward) of the parabola.