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What type of curves does the equation y = mx^3 + bx^2 + cx + d represent?

Practice Questions

Q1
What type of curves does the equation y = mx^3 + bx^2 + cx + d represent?
  1. Linear functions
  2. Quadratic functions
  3. Cubic functions
  4. Quartic functions

Questions & Step-by-Step Solutions

What type of curves does the equation y = mx^3 + bx^2 + cx + d represent?
  • Step 1: Identify the equation given, which is y = mx^3 + bx^2 + cx + d.
  • Step 2: Recognize that this equation is a polynomial equation of degree 3 because the highest power of x is 3.
  • Step 3: Understand that a polynomial of degree 3 is called a cubic function.
  • Step 4: Note that the coefficients m, b, c, and d can change, which means the shape of the curve can vary.
  • Step 5: Conclude that the equation represents a family of cubic curves, each defined by different values of m, b, c, and d.
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