Given a parabola $Y=X^2,$ how can I modify the equation so the parabola tilts away from it’s vertical orientation? For example, a solar collector might have a tilt of $23.5$ degrees. How would this look as a polynomial?

The parabola $y=x^2$ has a vertical axis. I will construe your $23.5^circ$ to mean $23.5^circ$ from the vertical.

You are watching: How to tilt a parabola

Draw the $x$-axis pointing to the right and the $y$-axis pointing upward.

Then draw a $u$-axis pointing in a direction $23.5^circ$ clockwise from the $x$-axis and a $v$-axis $23.5^circ$ clockwise from the $y$-axis.

You need the equation of your rotated parabola to be $v=u^2.$

We will need this:$$ ag 1egin{align}u & = (cos23.5^circ)x-(sin23.5^circ) y \v & = (sin23.5^circ)x +(cos23.5^circ) yend{align}$$

So $v=u^2$ becomes$$(sin23.5^circ)x +(cos23.5^circ) y = Big( (cos23.5^circ)x-(sin23.5^circ) y Big)^2.$$

For now I”ve left the derivation of $(1)$ as an exercise, but if necessary you can ask about that too.

See more: In Describing The Relationship Of The Thoracic And Spinal Cavities

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answered May 5 “18 at 19:44

Michael HardyMichael Hardy

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$endgroup$

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If your parabola is given by:

$$ -xsin a+ycos a =left( xcos a+ysin a-h

ight)^2+k $$

changing $h$ will move it along $x$ axis, changing $k$ will move it along the $y$ axis. Altering $a$ will tilt it.

See demo: https://www.desmos.com/calculator/hguanwbkbu

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answered May 5 “18 at 19:08

ITAITA

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