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Determine the family of curves represented by the equation y = kx^2, where k is
Determine the family of curves represented by the equation y = kx^2, where k is a constant.
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Practice Questions
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Q1
Determine the family of curves represented by the equation y = kx^2, where k is a constant.
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The equation y = kx^2 represents a family of parabolas that open upwards or downwards depending on the sign of k.
Questions & Step-by-step Solutions
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Q: Determine the family of curves represented by the equation y = kx^2, where k is a constant.
Solution:
The equation y = kx^2 represents a family of parabolas that open upwards or downwards depending on the sign of k.
Steps: 6
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Step 1: Identify the equation given, which is y = kx^2.
Step 2: Recognize that 'k' is a constant that can take different values.
Step 3: Understand that when k is positive (k > 0), the parabola opens upwards.
Step 4: Understand that when k is negative (k < 0), the parabola opens downwards.
Step 5: Note that for different values of k, you get different parabolas, but they all have the same basic shape.
Step 6: Conclude that the equation y = kx^2 represents a family of parabolas based on the value of k.
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