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What is the general form of the family of curves represented by the equation y =

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Question: What is the general form of the family of curves represented by the equation y = mx^2 + c?

Options:

  1. Parabolas
  2. Circles
  3. Ellipses
  4. Hyperbolas

Correct Answer: Parabolas

Solution: 

The equation y = mx^2 + c represents a family of parabolas that open upwards or downwards depending on the sign of m.

What is the general form of the family of curves represented by the equation y =

Practice Questions

Q1
What is the general form of the family of curves represented by the equation y = mx^2 + c?
  1. Parabolas
  2. Circles
  3. Ellipses
  4. Hyperbolas

Questions & Step-by-Step Solutions

What is the general form of the family of curves represented by the equation y = mx^2 + c?
  • Step 1: Identify the equation given, which is y = mx^2 + c.
  • Step 2: Recognize that 'm' is a coefficient that affects the shape of the curve.
  • Step 3: Understand that 'c' is a constant that shifts the curve up or down.
  • Step 4: Note that if 'm' is positive, the parabola opens upwards; if 'm' is negative, it opens downwards.
  • Step 5: Conclude that the equation represents a family of parabolas, each defined by different values of 'm' and 'c'.
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