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What type of curves does the equation y = kx^2 represent?
What type of curves does the equation y = kx^2 represent?
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Practice Questions
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Q1
What type of curves does the equation y = kx^2 represent?
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Parabolas with varying widths
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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
Q: What type of curves does the equation y = kx^2 represent?
Solution:
The equation y = kx^2 represents a family of parabolas that open upwards or downwards depending on the sign of 'k'.
Steps: 5
Show Steps
Step 1: Identify the equation given, which is y = kx^2.
Step 2: Recognize that this equation is in the form of a quadratic equation.
Step 3: Understand that a quadratic equation typically represents a curve called a parabola.
Step 4: Determine the role of 'k' in the equation. If 'k' is positive, the parabola opens upwards. If 'k' is negative, the parabola opens downwards.
Step 5: Conclude that the equation y = kx^2 represents parabolas that can either open upwards or downwards based on the value of 'k'.
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