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

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

Options:

  1. Parabolas
  2. Circles
  3. Ellipses
  4. Hyperbolas

Correct Answer: Parabolas

Solution: 

The equation y = a(x - h)^2 + k represents a family of parabolas with vertex (h, k).

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).
  • Quadratic Functions – The equation represents a quadratic function in vertex form, indicating the shape and position of parabolas.
  • Vertex of a Parabola – The vertex (h, k) is the highest or lowest point of the parabola, depending on the value of 'a'.
  • Parameter 'a' – The parameter 'a' determines the direction and width of the parabola (opening upwards or downwards).
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