# Week 8 : Properties of Quadratic Functions

This week we started with new lesson : Graphing Quadraction Functions about the determine the value of vertex, formula, what the graph looks like and how to draw the parabola.

So let’s start the things I studies in this week :

$y=ax^2+bx+c$ : It is general form of quadratic
With a (coefficent) it will helps us know the graph will be big or small.

Also, we can know : If quadratic positive $y=x^2$ , the parabola will be go up (+) and contrast if quadratic negative $y=-x^2$ , the parabola will go down.

It will be like this in graphing:

Vertex : highest and lowest point (-1,4)

Axis of Symmetry : which the parabola is symmetric (-1) of above picture

x-intercepts : zero of function or we can determine it by Quadractic Formula

y-intercepts : it depends on c

Maximum point : when the graph opens down Because the intersection point between x and y is at the top

Minimum point : when the graph opens up so the intersection point between x and y is at the bottom

Pattern of Parent Function :

$y=x^2$ it will show stretch / compress : 1,3,5,7,9..

But if $y=2x^2$ the stretch / compress : 2,4,6,10..

Domain : the value of x and the complete set of possible values of the independent variable, make sure it is real number.

Range : the value of y

$(x-p)^2$ : depends on the value of p, It will move to right or left

Let’s star with example :

$(x+7)^2$ : when p is positive the vertex move to left
$(x-7)^2$ : when p is negative the verter move to right