Math Problem Statement
Which of these options shows a correctly drawn quadratic graph?
Solution
The image shows four options (A, B, C, and D) for a quadratic graph, and the question asks which one is correctly drawn.
A correctly drawn quadratic graph should have the following characteristics:
- The graph is a parabola (U-shaped curve).
- If the quadratic term has a positive coefficient, the parabola opens upwards (concave up), and if negative, it opens downwards (concave down).
- The graph should have one vertex (minimum or maximum point) and could have one or two intersections with the x-axis (real roots).
- The graph should be symmetric about a vertical line through the vertex.
Analysis:
- Option A: The parabola is incorrectly drawn as the lines appear angular, not smooth, and doesn't resemble a quadratic graph.
- Option B: This graph shows a smooth, U-shaped curve, typical of a quadratic graph opening upwards, symmetric around the vertex.
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Math Problem Analysis
Mathematical Concepts
Quadratic Functions
Graphs of Parabolas
Formulas
Quadratic equation formula: ax^2 + bx + c = 0
Theorems
Symmetry of parabolas
Roots of quadratic equations
Suitable Grade Level
Grades 9-10
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