In Week 8 of Pre- Calc, we finally learned how to graph a parabola and label the parabola using the general form (or parent form) or the other formula which is . The first formula can go into the second formula to help you graph a parabola.

For the fomula  :

is the strench or compression of the parabola and it also indicates which way the parabola faces (up or down)

is where the parabola is on the y-axis (horizontal)

is where the parabola is on the x-axis (vertical)

These portions of the formula are also called translation.

*Using the second fomula you can find the Vertex (the tip of the parabola) using (p,q). Note that the q is part of the vertex and not the y-intercept in the parent formula which is the c in .

*You can also find out how much times the parabola touches the x-axis by using the discriminat (if its a positive number then it touches 2 times, if its a 0 then once and if its a negative number the 0 times)

We can find the vertex, axis of symmetry and the translation by looking at the parabola and applying it in

Vertex= (5,4)

Axis of Symmetry is x=5 (axis of symmetry is the line that goes straight through the parabola and makes it mirror each side)

The stretch of the parabola is because if you follow the basic 1,3,5,7 and multiply by 3 which would be 3,9,15,21 and you can see on the graph that it goes up by 3 first then 9 and so on. We also know that it a positive because it is facing up.

The parabola also moves 5 units to the right so it would be

*If it is adding then the parabalo moves to the left, if it is subtracting then in moves to the right. (opposite)

The parabola also moves 4 units up so it would be

Now we can apply what we know in the formula  which would be