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Vorde
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What is the maximum angle (degrees or radians) that you can rotate the basic parabola (y=x2) so that it can still be graphed as a function (y=...) with only one possible y-value per x-input.
Rotating a parabola around its axis does not change its overall shape. However, the specific location of the vertex and the direction of the opening may change depending on the angle of rotation.
The general equation for a rotated parabola is y = a(x-h)^2 + k, where a is the coefficient of the squared term, h and k are the coordinates of the vertex, and x and y are the coordinates of any point on the parabola.
The axis of rotation for a parabola is the line that passes through the vertex and is perpendicular to the parabola's axis of symmetry. It can be found by finding the slope of the line tangent to the parabola at the vertex and then using the negative reciprocal of that slope to find the perpendicular line.
No, a parabola cannot be rotated without changing its orientation. A rotation will always change the direction of the parabola's opening, even if the vertex remains in the same location.
Rotation of parabolas is commonly used in engineering and architecture to design structures such as bridges, arches, and domes. It can also be used in physics to model the motion of objects in projectile motion and in optics to determine the focal point of a curved mirror or lens.