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Find the equation of the axis of symmetry for the parabola y=x2−4x+1y = x^2 - 4x + 1. \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+1y = x^2 - 4x + 1. \newlineSimplify any numbers and write them as proper fractions, improper fractions, or integers.\newline__\_\_
  1. Identify coefficients: Identify the coefficients aa and bb from the quadratic equation y=ax2+bx+cy = ax^2 + bx + c. The given equation is y=x2−4x+1y = x^2 − 4x + 1, which can be compared to the standard form y=ax2+bx+cy = ax^2 + bx + c. Here, a=1a = 1 and b=−4b = -4.
  2. Calculate axis of symmetry: Use the formula for the axis of symmetry, which is x=−b2ax = -\frac{b}{2a}, to find the axis of symmetry for the parabola.\newlineSubstitute the values of aa and bb into the formula.\newlinex=−−42⋅1x = -\frac{-4}{2\cdot 1}\newlinex=42x = \frac{4}{2}\newlinex=2x = 2
  3. 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}.\newlineTherefore, the equation of the axis of symmetry for the given parabola is x=2x = 2.

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