All quadratic functions when graphed will have the shape of a parabola either opening up or down.

The parent function is adding different signs and numbers will change the shape and location of the graph. For example the coefficient of x will determine if the graph will be opening up or down. A positive coefficient will make the graph open upward and negative coefficients will make it open downward. This also helps with determine if the graph is a maximum or minimum, if it’s a positive coefficient it will be a minimum graph because it opens upward so the y values will increase on the other hand if it’s negative it would be  maximum graph because the highest y value will be at the top of the downward facing graph. The smaller the coefficient the more the graph will be compressed and the bigger they get the graph will become stretched and skinnier. To find the y intercept look at the end of the parent function in this case the y intercept is +3 (just put x value to zero  to find y int) when the point slides up or down it is called a vertical translation. When vertex slides left or right it is called horizontal translation (right or left).  if it’s subtracting a the graph will slide to the right or if it’s adding a it will slide to the left. Other terms used to describe a graph are vertex which is the starting place or change in direction. Axis of symmetry which is the x value the wold split the graph into 2 equal parts. Domain (x values) or range (y values).