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Basic Concepts: Quadratic function in vertex form: y = $a(x-p)^2 + q$, Converting from general to vertex form by completing the square, Shortcut: Vertex formula, Graphing parabolas for given quadratic functions

$p = \frac{1}{{4a}}$

- 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.a)$y = 2{x^2} - 12x + 10$b)${y^2} - 10y - 4x + 13 = 0$ - 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

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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