# Conics - Parabola

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##### Examples

###### Lessons

**vertical parabola VS. horizontal parabola**

Sketch the following vertical parabolas:

i) $y = {x^2}$

ii) $y = 2{x^2}$

iii) $y = 2{\left( {x + 3} \right)^2} + 1$- Sketch the following horizontal parabolas:

i) $x = {y^2}$

ii) $x = \frac{1}{2}{y^2}$

iii) $x = \frac{1}{2}{\left( {y - 1} \right)^2} - 3$ **converting quadratic functions to vertex form by "completing the square"**

Convert each quadratic function from general form to vertex form by completing the square.**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

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###### Topic Notes

**parabola:**a curve formed from all the points that are equidistant from the focus and the directrix.

**vertex**

**:**midway between the focus and the directrix

**focus**

**:**a point inside the parabola

**directrix**

**:**a line outside the parabola and perpendicular to the axis of symmetry

*conics formula for parabola:*$p = \frac{1}{{4a}}$

*p*: distance between the vertex and the focus / directrix.

*a*: coefficient of the squared term

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