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:

  1. The graph is a parabola (U-shaped curve).
  2. If the quadratic term has a positive coefficient, the parabola opens upwards (concave up), and if negative, it opens downwards (concave down).
  3. The graph should have one vertex (minimum or maximum point) and could have one or two intersections with the x-axis (real roots).
  4. 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