Understanding the Quadratic Equation: h(30) = 10 + 0.15(30) + 0.005(30)²

When evaluating mathematical expressions involving variables, quadratic equations often arise in science, engineering, and finance. One such example is the equation:

h(30) = 10 + 0.15(30) + 0.005(30)²

Understanding the Context

This formula represents a quadratic function, widely used to model relationships that change non-linearly. In this article, we’ll analyze the equation, compute h(30), and explore the significance of quadratic functions in practical applications.

What is a Quadratic Equation?

A quadratic equation takes the general form:

h(30) = 10 + 0,15(30) + 0,005(30)²

Key Insights

f(x) = ax² + bx + c

Where:

  • a, b, and c are constants,
  • x is the variable,
  • x² represents the squared term.

The presence of the x² term produces a parabolic shape—either open upward (if a > 0) or downward (if a < 0)—enabling modeling of curved relationships.

In the given expression:

  • a = 0.005
  • b = 0.15
  • c = 10
  • The input value is x = 30

Substitute into the formula:

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Final Thoughts

h(30) = 10 + 0.15(30) + 0.005(30)²

Step-by-Step Calculation of h(30)

  1. Compute 0.15 × 30
     0.15 × 30 = 4.5

  2. Compute (30)²:
     30² = 900

  3. Compute 0.005 × 900:
     0.005 × 900 = 4.5

  1. Now add all terms:
     h(30) = 10 + 4.5 + 4.5 = 19

Final result: h(30) = 19

Why This Equation Matters: Real-World Applications