Question: The family of curves y = ax^3 + bx^2 + cx + d is classified as:
Options:
Linear
Quadratic
Cubic
Quartic
Correct Answer: Cubic
Solution:
The equation y = ax^3 + bx^2 + cx + d represents a family of cubic curves.
The family of curves y = ax^3 + bx^2 + cx + d is classified as:
Practice Questions
Q1
The family of curves y = ax^3 + bx^2 + cx + d is classified as:
Linear
Quadratic
Cubic
Quartic
Questions & Step-by-Step Solutions
The family of curves y = ax^3 + bx^2 + cx + d is classified as:
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 because the highest power of x is 3.
Step 3: Understand that a polynomial of degree 3 is called a cubic polynomial.
Step 4: Conclude that since the equation represents a cubic polynomial, it describes a family of cubic curves.
Cubic Functions – The equation represents a cubic polynomial function, which is characterized by the highest degree of 3.
Family of Curves – The parameters a, b, c, and d define a family of curves, where varying these parameters changes the shape and position of the cubic graph.
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