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Find the equation of the axis of symmetry of the following parabola using graphing technology. y=4x^(2)+24 x+40 Answer:

Find the equation of the axis of symmetry of the following parabola using graphing technology.\newliney=4x2+24x+40 y=4 x^{2}+24 x+40 \newlineAnswer:

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Q. Find the equation of the axis of symmetry of the following parabola using graphing technology.\newliney=4x2+24x+40 y=4 x^{2}+24 x+40 \newlineAnswer:
  1. Identify General Form: Identify the general form of the quadratic equation.\newlineThe given parabola is in the form y=ax2+bx+cy = ax^2 + bx + c, where a=4a = 4, b=24b = 24, and c=40c = 40.
  2. Use Axis of Symmetry Formula: Use the formula for the axis of symmetry for a parabola in the form y=ax2+bx+cy = ax^2 + bx + c.\newlineThe axis of symmetry can be found using the formula x=−b2ax = -\frac{b}{2a}.
  3. Substitute Values: Substitute the values of aa and bb into the formula.x=−24(2⋅4)x = \frac{-24}{(2\cdot4)}x=−248x = \frac{-24}{8}x=−3x = -3
  4. Write Equation of Symmetry: Write the equation of the axis of symmetry.\newlineThe axis of symmetry is a vertical line, so its equation is x=constantx = \text{constant}.\newlineTherefore, the equation of the axis of symmetry is x=−3x = -3.

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