This week in pre-calculus 11, we learnt the equivalent forms of quadratic functions. There are 3 different types of functions: vertex/standard , general , and factored .

Each of these different functions will tell us something different about the graph and parabola; the standard for will give us the vertex, the general will give us the y-intercept and factored will give us the root or x-intercepts. All the functions “a” value will let us know if the parabola is congruent to the parent function, whether the parabola is a reflection, if it’s a minimum or maximum and whether it stretches or compresses. By knowing all the information from each function it will make graphing the parabola super easy.

Here is an example of changing general from to standard and factored.

To change it to standard form you need to complete the square like we did in the quadratic equation unit.

 

divide 3 out of first 2 terms

 

 

 

 

So, now we know the vertex of the parabola is (-1, -75)

Now if we want to change the general form to factored, something we can do to make it simpler is to find a greatest common factor within the function…

Once we have changed the general form to standard and factored we know: the vertex (-1,-75), the y-int (0,-72), the x-int (-6,0)/(4,0), the axis of symmetry (x=-1),that the graph is open faced, it is not congruent and that it has a stretch of 3,9,15