This is the plan that I have so far: The plan to achieve this goal is to first f

Question

This is the plan that I have so far:

The plan to achieve this goal is to first find the coefficients. Both of the equations are symmetrical to the y-axis, so the general equation would be y2=4ax. Since the banana opens upward, the coefficient a will be positive, hence the equation would be y2=4ax. The Gateway Arch is opened downward, so the coefficient a would be negative, hence the equation y2=-4ax.

a) I need to know how to find the coefficients to make the quadratic formula following this plan.

b) What dimensions do I apply to make the equation to draw a graph on graph paper i.e How do I use the dimensions for the realistic arc for the model for both the banana and the Gateway Arch? (Below are the pictures)

c) How do the dimensions relate to the graph drawn?

*Do you think the above mentioned plan is detailed enough to form a quadratic formula?*

Please help

Explanation / Answer

a) you already have the formula for both the figures that you mentioned above. That is the only formula where you do not need to put value of a. The formula will be in terms of a only.

b) To deaw the graph take any positive value of a for banana and any negative value of a say -1 for gateway arch then simply take any value of x positive or negative and find corresponding value of y and plot it on graph.

For different x value assumed you wull get different y , join all those point with a free hand anf you will get the required shape.

The above mentioned plan contains detailed explanation of forming quadratic equation or equation of parabola.

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