Conics - Parabola

Lessons

1. vertical parabola VS. horizontal parabola
   Sketch the following vertical parabolas:
   i) $y = {x^2}$
   ii) $y = 2{x^2}$
   iii) $y = 2{\left( {x + 3} \right)^2} + 1$
2. Sketch the following horizontal parabolas:
   i) $x = {y^2}$
   ii) $x = \frac{1}{2}{y^2}$
   iii) $x = \frac{1}{2}{\left( {y - 1} \right)^2} - 3$
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.
   1. $y = 2{x^2} - 12x + 10$
   2. ${y^2} - 10y - 4x + 13 = 0$
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
   
   1. $y = \frac{1}{8}{\left( {x - 6} \right)^2} + 3$
   2. $- 12\left( {x + 1} \right) = {\left( {y + 4} \right)^2}$
   3. ${y^2} - 10y - 4x + 13 = 0$