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Find the equation of the axis of symmetry for the parabola y=x2+2y = x^2 + 2. \newlineSimplify any numbers and write them as proper fractions, improper fractions, or integers.\newline__\_\_

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Q. Find the equation of the axis of symmetry for the parabola y=x2+2y = x^2 + 2. \newlineSimplify any numbers and write them as proper fractions, improper fractions, or integers.\newline__\_\_
  1. Identifying Quadratic Equation: The general form of a quadratic equation is y=ax2+bx+cy = ax^2 + bx + c. In the equation y=x2+2y = x^2 + 2, we can see that a=1a = 1, b=0b = 0, and c=2c = 2.
  2. Finding Axis of Symmetry: 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}. We will use the values of aa and bb that we found in the previous step to find the axis of symmetry.
  3. Calculating Axis of Symmetry: Substitute a=1a = 1 and b=0b = 0 into the formula x=−b2ax = -\frac{b}{2a} to find the axis of symmetry.\newlinex=−02×1x = -\frac{0}{2 \times 1}\newlinex=0x = 0
  4. Equation of Axis of Symmetry: The equation of the axis of symmetry is therefore x=0x = 0. This is a vertical line that passes through the vertex of the parabola.

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