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Find the equation of the axis of symmetry of the following parabola algebraically. y=2x^(2)-6 Answer:

Find the equation of the axis of symmetry of the following parabola algebraically.\newliney=2x2−6 y=2 x^{2}-6 \newlineAnswer:

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Q. Find the equation of the axis of symmetry of the following parabola algebraically.\newliney=2x2−6 y=2 x^{2}-6 \newlineAnswer:
  1. Quadratic Equation Form: The equation given is y=2x2−6y = 2x^2 - 6, which is a quadratic equation in the form y=ax2+bx+cy = ax^2 + bx + c, where a=2a = 2, b=0b = 0, and c=−6c = -6. Since there is no xx term (b=0b = 0), the parabola is symmetric about the yy-axis.
  2. Axis of Symmetry Formula: The axis of symmetry for a parabola in the form y=ax2+bx+cy = ax^2 + bx + c is given by the formula x=−b2ax = -\frac{b}{2a}. In this case, since b=0b = 0, the axis of symmetry is x=0x = 0.
  3. Equation of Axis of Symmetry: The equation of the axis of symmetry is therefore x=0x = 0, which is a vertical line passing through the origin and parallel to the yy-axis.

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