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Find the equation of the axis of symmetry for the parabola y=x2−x−8y = x^2 - x - 8. \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−8y = x^2 - x - 8. \newlineSimplify any numbers and write them as proper fractions, improper fractions, or integers.\newline_____\_\_\_\_\_
  1. Identify Coefficients: Identify the coefficients aa, bb, and cc in the quadratic equation y=ax2+bx+cy = ax^2 + bx + c. The given equation is y=x2−x−8y = x^2 - x - 8, which can be compared to y=ax2+bx+cy = ax^2 + bx + c. Here, a=1a = 1, b=−1b = -1, and c=−8c = -8.
  2. Use Axis of Symmetry Formula: Use the formula for the axis of symmetry, which is x=−b2ax = -\frac{b}{2a}, to find the axis of symmetry for the given parabola.\newlineSubstitute the values of aa and bb into the formula.\newlinex=−−12⋅1x = -\frac{-1}{2\cdot 1}\newlinex=12x = \frac{1}{2}
  3. Write Equation of Symmetry: Write the equation of the axis of symmetry.\newlineThe axis of symmetry is a vertical line, so its equation is of the form x=constantx = \text{constant}.\newlineTherefore, the equation of the axis of symmetry for the parabola y=x2−x−8y = x^2 − x − 8 is x=12x = \frac{1}{2}.

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