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Find the equation of the axis of symmetry for the parabola y=x22xy = x^2 - 2x. \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=x22xy = x^2 - 2x. \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 given parabola is y=x22xy = x^2 − 2x, which can be compared to the standard form y=ax2+bx+cy = ax^2 + bx + c.\newlineHere, a=1a = 1 and b=2b = -2. There is no cc term, so c=0c = 0.
  2. Use Axis of Symmetry Formula: Use the formula for the axis of symmetry.\newlineThe axis of symmetry for a parabola given by y=ax2+bx+cy = ax^2 + bx + c is x=b2ax = -\frac{b}{2a}.
  3. Substitute Values: Substitute the values of aa and bb into the formula.\newlineSubstitute a=1a = 1 and b=2b = -2 into the formula x=b/(2a)x = -b/(2a).\newlinex=(2)/(21)x = -(-2)/(2\cdot 1)\newlinex=2/2x = 2/2\newlinex=1x = 1
  4. 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=x22xy = x^2 − 2x is x=1x = 1.

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