Connections and differences between forms
Connections
Vertex form, standard form and completing the square are connected in several ways. The
most obvious connection being that standard form can be converted to vertex form
through completing the square. There are also little connections that we’ve been
over, such as the fact that “a” represents the same things in both vertex and
standard form. The quadratic equation also comes from completing the square, something that unites all these forms. While you can use x = -b/2a to solve an equation, the quadratic equation is still extremely helpful, due to the fact that it can give us our roots (x-intercepts), and the other equation only solves for the “x” of our vertex. To the left we see the equation x2 –4x – 8 = 0 being solved using the quadratic equation.
Vertex form, standard form and completing the square are connected in several ways. The
most obvious connection being that standard form can be converted to vertex form
through completing the square. There are also little connections that we’ve been
over, such as the fact that “a” represents the same things in both vertex and
standard form. The quadratic equation also comes from completing the square, something that unites all these forms. While you can use x = -b/2a to solve an equation, the quadratic equation is still extremely helpful, due to the fact that it can give us our roots (x-intercepts), and the other equation only solves for the “x” of our vertex. To the left we see the equation x2 –4x – 8 = 0 being solved using the quadratic equation.
Differences
Vertex form and standard form share differences along with their connections. In vertex form you are clearly able to see the vertex, while in standard form you are not. In standard form you can clearly see your y-intercept, while in vertex form you cannot. It’s also easier to use standard form to find your x-intercepts vs. using vertex form.
Vertex form and standard form share differences along with their connections. In vertex form you are clearly able to see the vertex, while in standard form you are not. In standard form you can clearly see your y-intercept, while in vertex form you cannot. It’s also easier to use standard form to find your x-intercepts vs. using vertex form.