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Find the equation of the axis of symmetry of the following parabola using graphing technology. y=-x^(2)+8x Answer:

Find the equation of the axis of symmetry of the following parabola using graphing technology.\newliney=−x2+8x y=-x^{2}+8 x \newlineAnswer:

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Q. Find the equation of the axis of symmetry of the following parabola using graphing technology.\newliney=−x2+8x y=-x^{2}+8 x \newlineAnswer:
  1. Identify Coefficients: The equation of a parabola in the form y=ax2+bx+cy = ax^2 + bx + c can have its axis of symmetry found using the formula x=−b2ax = -\frac{b}{2a}. Let's identify the coefficients aa and bb from the given equation y=−x2+8xy = -x^2 + 8x.
    a=−1a = -1 (coefficient of x2x^2)
    b=8b = 8 (coefficient of xx)
  2. Find Axis of Symmetry Formula: Now, we will use the formula x=−b2ax = -\frac{b}{2a} to find the axis of symmetry.\newlineSubstitute the values of aa and bb into the formula:\newlinex=−82×−1x = -\frac{8}{2 \times -1}
  3. Substitute Values: Perform the calculation:\newlinex=−8−2x = \frac{-8}{-2}\newlinex=4x = 4
  4. Perform Calculation: The equation of the axis of symmetry is a vertical line passing through the xx-coordinate we found. Therefore, the equation of the axis of symmetry is x=4x = 4.

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