This week we were learning about the properties of quadratic functions and we found out how to find those properties by looking at an equation.

Equation: the equation we use to find the parts of a graph is        y=$a(x-p)^2+q$

Vertex: The vertex is the most important thing to find because it leads to a lot of other parts in the graph.To find the vertex we look at the equation y=$a(x-p)^2+q$ and the coordinates of the vertex are (p,q)

Domain: Domain all possible values of x . Domain is always xER

Range: Range is all possible values of y. Need to graph the parabola  out to mak sure make the range is.

Minimum and Maximum: Minumum is when the coefficient of $x^2$ is positive and the parabola is opening up and the maximum is whe  the coefficient of $x^2$ is negative and the parabola is opening down

Axis of symmetry: the AOS is a line which goes right through the vertex. To find the AOS just need to have the p of the equation y=\$latex a(x-p)^2+q\$

Y intercept: is when the parabola passes through the y axis

X intercept: is when the parabola Passé through the x axis

Ex: y=$3(x-2)^2+1$

By using the  equation and graphing out the parabola we can find out that

Vertex = (2,1)

Domain= xER (because it will always be like this)

Range= Y is the sam or bigger than 1

opens up because the $x^2$ I positive

AOS= 2 because p in the equation is positive 2

Opening up

Minimum point

x int= none

y int= 13 because

$y=a(x-p)^2+q$ $y=3(0-2)^2+1$ $y=3(4)+1$ $y=12+1$

Y=13