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The family of curves defined by the equation y = a(x - h)^2 + k represents:

Practice Questions

Q1
The family of curves defined by the equation y = a(x - h)^2 + k represents:
  1. Parabolas
  2. Circles
  3. Ellipses
  4. Hyperbolas

Questions & Step-by-Step Solutions

The family of curves defined by the equation y = a(x - h)^2 + k represents:
  • Step 1: Identify the equation given, which is y = a(x - h)^2 + k.
  • Step 2: Recognize that this equation is in the form of a parabola.
  • Step 3: Understand that 'a' determines the direction and width of the parabola.
  • Step 4: Note that 'h' and 'k' represent the coordinates of the vertex of the parabola.
  • Step 5: Conclude that changing the value of 'a' will create different parabolas, but they will all have the same vertex at (h, k).
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