Here are the essential concepts you must grasp in order to answer the question correctly.
Parabola and its Vertex
A parabola is a symmetric curve defined by a quadratic equation. The vertex is the highest or lowest point of the parabola, depending on its orientation. For the equation given, rearranging it can help identify the vertex, which is crucial for determining the range of the relation.
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Direction of Opening
The direction in which a parabola opens (upward or downward) is determined by the coefficient of the squared term. In this case, since the equation is in the form of y^2, it indicates a sideways opening. This direction affects the domain and range of the relation, as it defines the set of possible x and y values.
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Function Definition
A relation is considered a function if each input (x-value) corresponds to exactly one output (y-value). In the context of the given equation, analyzing whether it passes the vertical line test will help determine if it is a function. If a vertical line intersects the graph at more than one point, it is not a function.
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Graphs of Common Functions