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Find the equation of the axis of symmetry for the parabola y=x2+x+2y = x^2 + x + 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+x+2y = x^2 + x + 2. \newlineSimplify any numbers and write them as proper fractions, improper fractions, or integers.\newline_____\_\_\_\_\_
  1. Identify Quadratic Equation: The general form of a quadratic equation is y=ax2+bx+cy = ax^2 + bx + c. To find the axis of symmetry, we use the formula x=−b2ax = -\frac{b}{2a}.\newlineFor the given parabola y=x2+x+2y = x^2 + x + 2, we can identify a=1a = 1 and b=1b = 1 by comparing it to the general form.
  2. Calculate Axis of Symmetry: Now we substitute the values of aa and bb into the formula for the axis of symmetry.x=−b2a=−12⋅1=−12x = -\frac{b}{2a} = -\frac{1}{2\cdot 1} = -\frac{1}{2}
  3. Equation of Axis of Symmetry: The equation of the axis of symmetry is therefore x=−12x = -\frac{1}{2}. This is a vertical line that passes through the point (−12,y)(-\frac{1}{2}, y) for all values of yy.

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