Question

graphing the clifton suspension bridge
edit the equation to transform the parabola to fit
the bridge. restrict the domain.
$y = 0.038x^2 - 2\\{-10\leq x\leq 10\\}$

Explanation:

Step1: Analyze the x-intercept

We know one x - intercept is \(x = 7.25476\). Since the parabola is symmetric about the y - axis (the coefficient of \(x^2\) is positive and there is no \(x\) term), the other x - intercept should be \(x=- 7.25476\). So the domain should be restricted between \(-7.25476\) and \(7.25476\) to fit the bridge.

Step2: Adjust the equation's domain

The original equation is \(y = 0.038x^{2}-2\) with domain \(-10\leq x\leq10\). We need to change the domain to \(-7.25476\leq x\leq7.25476\) so that the parabola fits the bridge (since the bridge's base is between the two x - intercepts of the parabola representing it).

Answer:

The equation with the correct domain restriction is \(y = 0.038x^{2}-2\) where \(-7.25476\leq x\leq7.25476\) (or a more approximate form like \(-7.25\leq x\leq7.25\) depending on the required precision).