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The family of curves represented by the equation y = kx^2, where k is a constant

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Question: The family of curves represented by the equation y = kx^2, where k is a constant, is known as:

Options:

  1. Linear curves
  2. Parabolic curves
  3. Circular curves
  4. Exponential curves

Correct Answer: Parabolic curves

Solution: 

The equation y = kx^2 represents a parabola for different values of k.

The family of curves represented by the equation y = kx^2, where k is a constant

Practice Questions

Q1
The family of curves represented by the equation y = kx^2, where k is a constant, is known as:
  1. Linear curves
  2. Parabolic curves
  3. Circular curves
  4. Exponential curves

Questions & Step-by-Step Solutions

The family of curves represented by the equation y = kx^2, where k is a constant, is known as:
  • Step 1: Identify the equation given, which is y = kx^2.
  • Step 2: Understand that 'k' is a constant that can take different values.
  • Step 3: Recognize that for each value of 'k', the shape of the graph changes but remains a specific type of curve.
  • Step 4: Realize that the shape of the graph for the equation y = kx^2 is a parabola.
  • Step 5: Conclude that the family of curves represented by this equation is known as parabolas.
  • Parabola – The equation y = kx^2 describes a family of parabolas that open upwards for k > 0 and downwards for k < 0.
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