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Find the equation of the axis of symmetry for the parabola y=x2−3x+4y = x^2 - 3x + 4. \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=x2−3x+4y = x^2 - 3x + 4. \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 by y=ax2+bx+cy = ax^2 + bx + c. For the parabola y=x2−3x+4y = x^2 − 3x + 4, we can compare it to the standard form and identify the coefficients as follows:\newlinea=1a = 1 (coefficient of x2x^2)\newlineb=−3b = -3 (coefficient of xx)\newlinec=4c = 4 (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: Substitute the values of aa and bb into the formula.a=1a = 1b=−3b = -3x=−(−3)/(2⋅1)x = -(-3)/(2\cdot1)x=32x = \frac{3}{2}The axis of symmetry is therefore x=32x = \frac{3}{2}.

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