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The vertex of a parabola is located at \( (-3 \), \( 0) \). What would be the axis of symmetry? Draw a picture if you have to. Type a response

Ask by Ellis Sandoval. in the United States
Mar 09,2025

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The axis of symmetry is the vertical line \( x = -3 \).

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The vertex of the parabola is at \( (-3, 0) \). For any parabola, the axis of symmetry is a vertical line that passes through the vertex. This means the equation of the axis of symmetry is: \[ x = -3 \] Here is a simple diagram illustrating the vertex and the axis of symmetry: \[ \begin{array}{c} \text{Axis of symmetry: } x = -3 \\ \quad\quad\quad\quad\quad\quad | \\ \quad\quad\quad\quad\quad\quad | \\ \quad\quad\quad (-3, 0)\bullet \quad\quad\text{(Vertex)} \\ \quad\quad\quad\quad\quad\quad | \\ \quad\quad\quad\quad\quad\quad | \\ \end{array} \] Thus, the axis of symmetry for the parabola is \( x = -3 \).

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The axis of symmetry for a parabola is a vertical line that passes through the vertex. Since the vertex is located at \( (-3, 0) \), the axis of symmetry can be expressed as the line \( x = -3 \). This means that if you were to fold the parabola along this line, both sides would be mirror images of each other. Imagine your parabola opens either upwards or downwards from this vertex point. To visualize it, draw a vertical dashed line at \( x = -3 \). On both sides of this line, you'll see the curve of the parabola taking shape, perfectly symmetrical around that vertical axis!

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