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What type of curves does the equation y = mx^3 + bx^2 + cx + d represent?
What type of curves does the equation y = mx^3 + bx^2 + cx + d represent?
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Practice Questions
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Q1
What type of curves does the equation y = mx^3 + bx^2 + cx + d represent?
Linear functions
Quadratic functions
Cubic functions
Quartic functions
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The equation y = mx^3 + bx^2 + cx + d represents a family of cubic functions with varying coefficients.
Questions & Step-by-step Solutions
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Q
Q: What type of curves does the equation y = mx^3 + bx^2 + cx + d represent?
Solution:
The equation y = mx^3 + bx^2 + cx + d represents a family of cubic functions with varying coefficients.
Steps: 5
Show Steps
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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