To identify the vertex and axis of symmetry of the parabola defined by the points (0, 50), (-20, 50), and (-10, 0), we can follow these steps:
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Determine the shape of the parabola: We note two points on the parabola, (0, 50) and (-20, 50), both of which have the same \(y\) value. This indicates that these points are symmetrical about the axis of symmetry. The third point (-10, 0) is the lowest point if the parabola opens upward or the highest if it opens downward, but we will confirm this based on the minimum \(y\) value.
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Finding the axis of symmetry: The axis of symmetry will be midway between the points (0, 50) and (-20, 50). The \(x\) coordinate of the axis can be found as follows:
\[ x = \frac{-20 + 0}{2} = -10 \]
Thus, the axis of symmetry is \(x = -10\).
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Identifying the vertex: Since (-10, 0) is a point on the parabola and is directly on the axis of symmetry we determined, this point is also the vertex of the parabola.
So, we have:
- Vertex: \((-10, 0)\)
- Axis of Symmetry: \(x = -10\)
In conclusion, the vertex of the parabola is (-10, 0), and its axis of symmetry is \(x = -10\).