​Quadratic Relationships

In vertex form you have many things that are apart of it. Firstly, you have the axis of symmetry and what this is, is basically the vertex of the graph so you would take the x-intercepts add them together and divide them by two to find the x value of the vertex, then you would sub in your x value into the equation and isolate for y, then after yoou found both x and y you would plot your vertex.

 

Secondly, you have Optimal value and this is basically the max or min value of the parobala. If the parobala opens downwards then the optimal value will be the max of the parobala, if the parobala opens upwards then the optimal value is the min of the parobala.

 

Next you have transformations. These are your vertical & horizontal translations, your vertical stretch and your reflection. Starting with vertical and horizontal translations, so translating a graph means that the graph is either moving vertically or horizontally around the coordinate plane. Vertical translation means its either going to move up or down & horizontal translation means its either going to go left or right depending on the situation.

 

Now you have vertical stretch. Vertical stretch is where the grah is stretching away from the x axis. Next you have the x intercepts, these are the points on the x axis and where youll start to graph your parobola. To find the x intecepts you just let y be 0 & solve for x. Finally you have the step pattern