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Find the equation of the axis of symmetry for the parabola y=x2−7x+9y = x^2 - 7x + 9. \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=x2−7x+9y = x^2 - 7x + 9. \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=x2−7x+9y = x^2 − 7x + 9, we can identify the coefficients as follows:\newlinea=1a = 1 (coefficient of x2x^2)\newlineb=−7b = -7 (coefficient of xx)\newlinec=9c = 9 (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.\newlinea=1a = 1\newlineb=−7b = -7\newlinex=−(−7)/(2⋅1)x = -(-7)/(2 \cdot 1)\newlinex=72x = \frac{7}{2}
  4. Simplify to Find Axis: Simplify the expression to find the axis of symmetry. \newlinex=72x = \frac{7}{2}\newlineThis is already simplified and represents the equation of the axis of symmetry for the given parabola.

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