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Find the equation of the axis of symmetry of the following parabola algebraically. y=-3x^(2)+18 x-21 Answer:

Find the equation of the axis of symmetry of the following parabola algebraically.\newliney=−3x2+18x−21 y=-3 x^{2}+18 x-21 \newlineAnswer:

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Q. Find the equation of the axis of symmetry of the following parabola algebraically.\newliney=−3x2+18x−21 y=-3 x^{2}+18 x-21 \newlineAnswer:
  1. Identify Coefficients: The equation of a parabola in the form y=ax2+bx+cy = ax^2 + bx + c can have its axis of symmetry found using the formula x=−b2ax = -\frac{b}{2a}.
  2. Apply Formula: First, identify the coefficients aa and bb from the given quadratic equation y=−3x2+18x−21y = -3x^2 + 18x - 21. Here, a=−3a = -3 and b=18b = 18.
  3. Calculate Axis of Symmetry: Now, apply the formula for the axis of symmetry using the values of aa and bb.x=−b2a=−182×−3=−18−6=3.x = \frac{-b}{2a} = \frac{-18}{2 \times -3} = \frac{-18}{-6} = 3.
  4. Final Result: The equation of the axis of symmetry is therefore x=3x = 3.

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