In this unit we learned how to graph a parabola using a quadratic function. There are three different forms that you can write a quadratic function: Vertex form which is y=a(x-p)²-q, Standard form which is y=ax²+bx+c, the last one is Factored form which is y=a(x1-x1)(x2-x2).
All three functions gives you different information. The vertex form gives you the most important part of the parabola which is the vertex, using the vertex you can find the line of symmetry so you can say that it gives you the line of symmetry, and the stretch. The standard form gives you the y intercept and the stretch. The factored form gives you the x intercepts and the stretch.
Sometimes you will be required to convert an equation to a different form in order to find a different piece of information. So In order to go from standard form to vertex form you need to complete the square. In order to go from vertex form to standard form you need to expand. In order to go from standard form to factored you have to factor. In order to go from factored form to standard you need to expand.
vertex form <—-> Standard form <—-> Factored form
You cannot go from factored form to vertex form and vice versa
Example:
Vertex Form: y = 8 (x – 7)² – 4
Standard Form: y = 8x² – 112x +388
Factored Form: Not factorable
Opens up
Minimum
Vertex: (7,-4)
Line of symmetry: x = 7
Stretch: 8
Y intercept: (0,388)
X intercept: (6.293,0) , (7.707,0)
