This week in pre-calc we learned how to analyzing quadratic functions in the form of graphs using the equation

$y=a(x-p)^2+q$

The vertex is found easily with this as the p variable is what ends up being the x value and the q variable being the y value in the vertex.

With the vertex we can then find the axis of symmetry.

With the coefficient of x (a being the variable of whatever the coefficient is) we can figure out if its maximum or minimum vertex if it’s negative or positive, if minimum it opens upward and if maximum it opens downwards. Using the information of the equation we can figure out what its congruent to as well as the rest of the information needed such as x/y intercepts and domain and range