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What type of curves does the equation y = kx^2 represent?

Practice Questions

Q1
What type of curves does the equation y = kx^2 represent?
  1. Straight lines
  2. Parabolas with varying widths
  3. Circles
  4. Ellipses

Questions & Step-by-Step Solutions

What type of curves does the equation y = kx^2 represent?
  • 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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