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Find the equation of the axis of symmetry for the parabola y=x2−4x−2y = x^2 - 4x - 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=x2−4x−2y = x^2 - 4x - 2. \newlineSimplify any numbers and write them as proper fractions, improper fractions, or integers.\newline_____
  1. Identify Coefficients: Identify the coefficients of the quadratic equation.\newlineThe quadratic equation is given in the form y=ax2+bx+cy = ax^2 + bx + c. For the parabola y=x2−4x−2y = x^2 - 4x - 2, we can identify the coefficients as follows:\newlinea=1a = 1 (coefficient of x2x^2)\newlineb=−4b = -4 (coefficient of xx)\newlinec=−2c = -2 (constant term)
  2. Use Axis of Symmetry Formula: Use the formula for the axis of symmetry.\newlineThe axis of symmetry for a parabola given by the equation y=ax2+bx+cy = ax^2 + bx + c is x=−b2ax = -\frac{b}{2a}. We will substitute the values of aa and bb into this formula to find the axis of symmetry.
  3. Substitute Values into Formula: Substitute the values of aa and bb into the formula.\newlineUsing the values from Step 11, we have:\newlinea=1a = 1\newlineb=−4b = -4\newlineNow, substitute these values into the formula x=−b/(2a)x = -b/(2a):\newlinex=−(−4)/(2⋅1)x = -(-4)/(2\cdot 1)\newlinex=4/2x = 4/2\newlinex=2x = 2
  4. Write Equation of Axis: 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}. From Step 33, we found that the constant is 22. Therefore, the equation of the axis of symmetry is:\newlinex=2x = 2

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