Check the solution to "How to find the coefficient a of ay=ax2parabola?"

Bruce Rosario

Answered question

2022-04-22

How to find the coefficient a of a

y = a x^{2}

parabola?

Answer & Explanation

Ezakhenitne

Beginner2022-04-23Added 10 answers

Step 1
As a first qualitative step we know that if the parabola opens upward

a > 0

otherwise if it opens downward

a < 0

For a quantitative evaluation we need at least to know the coordinates of a point

(x_{0}, y_{0})

on the parabola with

x_{0} \neq 0

and then

y_{0} = a x_{0}^{2} \Rightarrow a = \frac{y_{0}}{x_{0}^{2}}

Brenton Steele

Beginner2022-04-24Added 18 answers

Hold your parabolic mirror in a vertical position, with some distant object in front of it (the Sun, a tall tree with the sky as background, and so on) and a vertical white screen where to project the image.
Move your mirror until the image formed on the screen is clear and detailed. Measure then the distance between the image on the screen and the center of your mirror: that is the focal distance f of your screen. And

a = \frac{1}{4 f}

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