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What is the general form of the family of curves represented by the equation y =
What is the general form of the family of curves represented by the equation y = mx^2 + c?
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What is the general form of the family of curves represented by the equation y = mx^2 + c?
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The equation y = mx^2 + c represents a family of parabolas that open upwards or downwards depending on the sign of m.
Questions & Step-by-step Solutions
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Q: What is the general form of the family of curves represented by the equation y = mx^2 + c?
Solution:
The equation y = mx^2 + c represents a family of parabolas that open upwards or downwards depending on the sign of m.
Steps: 5
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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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