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Find the equation of the axis of symmetry of the following parabola algebraically.

y=-x^(2)+4x-2
Answer:

Find the equation of the axis of symmetry of the following parabola algebraically.\newliney=x2+4x2 y=-x^{2}+4 x-2 \newlineAnswer:

Full solution

Q. Find the equation of the axis of symmetry of the following parabola algebraically.\newliney=x2+4x2 y=-x^{2}+4 x-2 \newlineAnswer:
  1. Identify Equation Parameters: The equation of a parabola in the form y=ax2+bx+cy = ax^2 + bx + c has an axis of symmetry that can be found using the formula x=b2ax = -\frac{b}{2a}. In our equation, y=x2+4x2y = -x^2 + 4x - 2, we identify a=1a = -1 and b=4b = 4.
  2. Calculate Axis of Symmetry: We substitute the values of aa and bb into the formula for the axis of symmetry.x=b2a=42(1)=42=2.x = \frac{-b}{2a} = \frac{-4}{2*(-1)} = \frac{-4}{-2} = 2.
  3. Determine Axis of Symmetry: The equation of the axis of symmetry is therefore x=2x = 2. This is a vertical line that passes through the vertex of the parabola.

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