Math Problem Statement
Solution
The image shows a graph of a quadratic function and several questions related to its properties. The function appears to be a parabola, and the tasks involve determining intervals of increase/decrease and possibly identifying key features like the vertex, axis of symmetry, and range.
To proceed, let's analyze the graph and the questions:
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Vertex: The vertex of the parabola is the highest or lowest point, depending on the direction the parabola opens. Since this parabola opens upwards (as indicated by the U-shape), the vertex is the minimum point.
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Increasing/Decreasing Intervals:
- The graph is decreasing on the interval from negative infinity to the x-coordinate of the vertex.
- The graph is increasing on the interval from the x-coordinate of the vertex to positive infinity.
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Range: The range of the function will be from the y-coordinate of the vertex to positive infinity (since the parabola opens upwards).
Analysis Steps:
- Locate the vertex on the graph to determine the exact coordinates.
- Identify the axis of symmetry, which passes through the vertex (it will be vertical).
- Determine the intervals where the function is increasing and decreasing.
- Calculate the range using the y-coordinate of the vertex.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Functions
Graph Analysis
Formulas
Vertex Formula: x = -b/(2a)
Quadratic Function: f(x) = ax^2 + bx + c
Theorems
Properties of Parabolas
Symmetry of Parabolas
Suitable Grade Level
Grades 8-10
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