A parabola is a U-shaped plane curve that is represented by a quadratic equation of the form y = ax^2 + bx + c, where a, b, and c are constants. A parabola is a symmetrical curve, which means that it has a specific and fixed axis (a point) of symmetry that splits the curve into two similar-looking mirror images.
The axis of symmetry of a parabola is a straight line that runs through the center of the parabola and is perpendicular to the directrix (the line that is symmetrical about the parabola). This is the line that the parabola would fold over onto itself if it were folded along this line.
The axis of symmetry of a parabola can be found using the following formula:
x = -b/(2a)
In which, x is the coordinate of the axis of symmetry, and, a and b are the constants from the parabola equation.
As an example, suppose, the parabola y = 2x^2 - 3x + 4. The axis of symmetry for this parabola can be calculated by adding the values of a and b into the formula:
x = -(-3)/(2*2) = 3/4
It implies that the axis of symmetry of the parabola y = 2x^2 - 3x + 4 is the line x = 3/4.
The axis of symmetry is a significant property of a parabola, and it is applied in many places, like in engineering and physics to replicate the path of objects under the influence of gravity.
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