What do the variables in parabola equations represent?

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What do the variables in parabola equations represent?

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Answer 1 · 2017-12-21T15:21:41

Please see below.

Explanation:

General equation of parabola is of the form $y = a {(x - h)}^{2} + k$ $y=a(x-h)^2+k$ or $x = a {(y - k)}^{2} + h$ $x=a(y-k)^2+h$ . Former is known as verticle parabola and latter is known as horizontal parabola.

In both cases vertex is $(h, k)$ $(h,k)$ ,

axis of symmetery is $x - h = 0$ $x-h=0$ in former case and $y - k = 0$ $y-k=0$ in latter case.

Focii are $(h, k + \frac{1}{4 a})$ $(h,k+1/(4a))$ in former case and $(h + \frac{1}{4 a}, k)$ $(h+1/(4a),k)$ in latter case.

Directrix is $y = k - \frac{1}{4 a}$ $y=k-1/(4a)$ in former case and $x = h - \frac{1}{4 a}$ $x=h-1/(4a)$ in latter case.

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What do the variables in parabola equations represent?

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