Math Problem Statement

Match the number and type of solutions based on the graphs of quadratic equations.

Solution

The image contains a set of graphs of quadratic equations with parabolas, where the task is to match the number and type of solutions (real or non-real) to the given equations based on the graphs. Here’s how the solutions are determined:

  1. Two Real Solutions: The parabola intersects the x-axis at two distinct points.
  2. One Real Solution: The parabola touches the x-axis at exactly one point (the vertex lies on the x-axis).
  3. Two Non-real Solutions (Complex): The parabola does not intersect the x-axis at all.

Would you like me to provide detailed matches for each graph in the image? If yes, let me know!

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Math Problem Analysis

Mathematical Concepts

Quadratic Equations
Graphing Parabolas
Roots of Equations

Formulas

Quadratic equation formula: ax^2 + bx + c = 0

Theorems

Nature of Roots (Discriminant-based classification)
Graphical Representation of Roots

Suitable Grade Level

Grades 7-9