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Find the equation of the axis of symmetry of the following parabola using graphing technology. y=-x^(2)-7 Answer:

Find the equation of the axis of symmetry of the following parabola using graphing technology.\newliney=−x2−7 y=-x^{2}-7 \newlineAnswer:

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Q. Find the equation of the axis of symmetry of the following parabola using graphing technology.\newliney=−x2−7 y=-x^{2}-7 \newlineAnswer:
  1. Identify Parabola Equation: The equation of the parabola is given by y=−x2−7y = -x^2 - 7. To find the axis of symmetry, we need to identify the vertex of the parabola. The standard form of a quadratic equation is y=ax2+bx+cy = ax^2 + bx + c. In this case, a=−1a = -1, b=0b = 0, and c=−7c = -7. Since the coefficient bb is 00, the vertex lies on the y-axis, and the axis of symmetry is a vertical line through the vertex.
  2. Find Vertex and Coefficients: The axis of symmetry for a parabola in the form y=ax2+bx+cy = ax^2 + bx + c is given by the line x=−b2ax = -\frac{b}{2a}. In our case, since b=0b = 0, the axis of symmetry is x=02(−1)=0x = \frac{0}{2(-1)} = 0.
  3. Calculate Axis of Symmetry: The equation of the axis of symmetry is therefore the vertical line x=0x = 0, which is the y-axis itself.

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