To provide a specific answer, I would need to see the graph you’re referring to, as different graphs can lead to different interpretations. However, I can give you general guidelines based on common characteristics of quadratic graphs (parabolas):
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Vertex: The vertex of a parabola is either a maximum or minimum point, depending on whether it opens upwards or downwards.
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Direction: If the parabola opens upwards (the coefficient of the \(x^2\) term is positive), the vertex is the minimum point. If it opens downwards (the coefficient of the \(x^2\) term is negative), the vertex is the maximum point.
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Intercepts: The points where the parabola intersects the y-axis (y-intercept) can be found by setting \(x = 0\) in the equation of the quadratic. The x-intercepts (roots) can be found by setting the quadratic equation to zero and solving for x.
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Axis of Symmetry: A parabola is symmetric about a vertical line known as the axis of symmetry, which can be found using \(x = -\frac{b}{2a}\) if the quadratic is in the standard form \(y = ax^2 + bx + c\).
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End Behavior: For large values of \(x\), the behavior of the quadratic function is dominated by the \(x^2\) term—if \(a > 0\), as \(x\) approaches infinity, \(y\) approaches infinity. If \(a < 0\), \(y\) approaches negative infinity.
If you have specific statements or observations based on the graph, feel free to share them, and I can help you determine which one is true!
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