Math Problem Statement

Is this a quadratic??

Is this a quadratic?

Solution

Let's analyze the two given equations:

  1. y=2(x2+3)y = 2(x^2 + 3)
  2. y=x2(6+x)y = x^2(6 + x)

First Equation: y=2(x2+3)y = 2(x^2 + 3)

This equation can be expanded as: y=2x2+6y = 2x^2 + 6 Here, the highest degree of the variable xx is 2, making this a quadratic equation. So, yes, the first equation is quadratic.

Second Equation: y=x2(6+x)y = x^2(6 + x)

Expanding this equation: y=6x2+x3y = 6x^2 + x^3 In this case, the highest degree of the variable xx is 3, which makes it a cubic equation, not quadratic.

Conclusion:

  • The first equation is quadratic.
  • The second equation is cubic.

Would you like further details or explanations on any part?

Here are 5 related questions to explore:

  1. How can you identify a quadratic equation by its form?
  2. What are the key features of quadratic functions (e.g., vertex, axis of symmetry)?
  3. How do cubic equations differ in graph shape from quadratic equations?
  4. Can a quadratic equation have complex roots?
  5. How does the factorization of quadratic equations work?

Tip: A quadratic equation will always have a degree of 2, meaning the highest power of xx is x2x^2.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations
Cubic Equations

Formulas

Quadratic equation y = ax^2 + bx + c
Cubic equation y = ax^3 + bx^2 + cx + d

Theorems

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Suitable Grade Level

Grades 9-11