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Determine the family of curves represented by the equation y = ax^3 + bx^2 + cx
Determine the family of curves represented by the equation y = ax^3 + bx^2 + cx + d.
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Practice Questions
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Q1
Determine the family of curves represented by the equation y = ax^3 + bx^2 + cx + d.
Cubic functions
Quadratic functions
Linear functions
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The equation y = ax^3 + bx^2 + cx + d represents a family of cubic functions.
Questions & Step-by-step Solutions
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Q: Determine the family of curves represented by the equation y = ax^3 + bx^2 + cx + d.
Solution:
The equation y = ax^3 + bx^2 + cx + d represents a family of cubic functions.
Steps: 5
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Step 1: Identify the equation given, which is y = ax^3 + bx^2 + cx + d.
Step 2: Recognize that this equation is a polynomial of degree 3, which is called a cubic function.
Step 3: Note that 'a', 'b', 'c', and 'd' are constants that can change, which means they can take different values.
Step 4: Understand that changing the values of 'a', 'b', 'c', and 'd' will create different shapes of the cubic curve.
Step 5: Conclude that all the different shapes created by varying 'a', 'b', 'c', and 'd' represent a family of curves.
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