Q. Find the equation of the axis of symmetry of the following parabola algebraically.y=−x2+4x−2Answer:
Identify Equation Parameters: The equation of a parabola in the form y=ax2+bx+c has an axis of symmetry that can be found using the formula x=−2ab. In our equation, y=−x2+4x−2, we identify a=−1 and b=4.
Calculate Axis of Symmetry: We substitute the values of a and b into the formula for the axis of symmetry.x=2a−b=2∗(−1)−4=−2−4=2.
Determine Axis of Symmetry: The equation of the axis of symmetry is therefore x=2. This is a vertical line that passes through the vertex of the parabola.
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