To identify the vertex and axis of symmetry of a parabola, we typically start with the standard form of a quadratic equation, \( y = ax^2 + bx + c \).
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Axis of symmetry: The formula for the axis of symmetry of a parabola given by the equation \( y = ax^2 + bx + c \) is: \[ x = -\frac{b}{2a} \]
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Vertex: The vertex can be found using the axis of symmetry. Once we calculate \( x \) from the axis of symmetry, we can substitute it back into the equation to find the \( y \)-coordinate of the vertex: \[ y = a\left(-\frac{b}{2a}\right)^2 + b\left(-\frac{b}{2a}\right) + c \] This gives the coordinates of the vertex as: \[ \left(-\frac{b}{2a}, y\right) \]
If you provide the quadratic equation, I can help you calculate the vertex and the axis of symmetry specifically for that parabola.