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Find the equation of the axis of symmetry of the following parabola algebraically. y=4x^(2)-64 x+248 Answer:

Find the equation of the axis of symmetry of the following parabola algebraically.\newliney=4x2−64x+248 y=4 x^{2}-64 x+248 \newlineAnswer:

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Q. Find the equation of the axis of symmetry of the following parabola algebraically.\newliney=4x2−64x+248 y=4 x^{2}-64 x+248 \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}.
  2. Apply Formula: First, identify the coefficients aa and bb from the given equation y=4x2−64x+248y = 4x^2 - 64x + 248. Here, a=4a = 4 and b=−64b = -64.
  3. Substitute Values: Now, apply the formula x=−b2ax = -\frac{b}{2a} to find the axis of symmetry.\newlineSubstitute a=4a = 4 and b=−64b = -64 into the formula to get x=−−642×4x = -\frac{-64}{2 \times 4}.
  4. Calculate Value: Calculate the value of x=642×4x = \frac{64}{2 \times 4}.\newlineThis simplifies to x=648x = \frac{64}{8}.
  5. Find Axis of Symmetry: After simplifying, we find that x=8x = 8. This is the equation of the axis of symmetry for the given parabola.

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