Conics - Parabola

Lessons

• 1.
  vertical parabola VS. horizontal parabola
  Sketch the following vertical parabolas:
  i) $y = {x^2}$
  ii) $y = 2{x^2}$
  iii) $y = 2{\left( {x + 3} \right)^2} + 1$

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• 2.
  Sketch the following horizontal parabolas:
  i) $x = {y^2}$
  ii) $x = \frac{1}{2}{y^2}$
  iii) $x = \frac{1}{2}{\left( {y - 1} \right)^2} - 3$

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• 3.
  converting quadratic functions to vertex form by "completing the square"
  Convert each quadratic function from general form to vertex form by completing the square.
  a)

  $y = 2{x^2} - 12x + 10$
  
  
  b)

  ${y^2} - 10y - 4x + 13 = 0$
  
  

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• 4.
  finding the focus and directrix using the formula: $p = \frac{1}{{4a}}$
  For each quadratic function, state the:
  i) vertex
  ii) axis of symmetry
  iii) focus
  iv) directrix
  
  a)

  $y = \frac{1}{8}{\left( {x - 6} \right)^2} + 3$
  
  
  b)

  $- 12\left( {x + 1} \right) = {\left( {y + 4} \right)^2}$
  
  
  c)

  ${y^2} - 10y - 4x + 13 = 0$
  
  

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