Math Problem Statement

Write the equation of the parabola shown in the graph. Write your answer in the form y=a(x–p)(x–q), where a, p, and q are integers, decimals, or simplified fractions.

Solution

To write the equation of a parabola in the form y=a(xp)(xq)y = a(x - p)(x - q), we need to identify the following components from the graph:

  1. The x-intercepts (roots): These are the points where the parabola crosses the x-axis. These values will correspond to pp and qq.
  2. The coefficient aa: This controls the direction and width of the parabola. If the parabola opens upward, aa will be positive, and if it opens downward, aa will be negative.

Please upload the graph of the parabola so I can help you identify these components and write the equation.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations
Parabolas
Factoring

Formulas

y = a(x - p)(x - q)

Theorems

Factoring of quadratics
Roots of quadratic equations

Suitable Grade Level

Grades 9-12