Parabolas that "open up" have a "cup" orientation, like [tex]\cup[/tex], and parabolas that "open down" have a "cap" orientation, like [tex]\cap[/tex].
The equation is in the standard form [tex]y=ax^2+bx+c
[/tex].
To graph the parabola, we need its vertex and another point on the parabola.
The vertex can be found using the formula for the x-coordinate, [tex] \dfrac{-b}{2a} [/tex].
The other point can be the y-intercept, which in standard form is simply [tex](0,c)[/tex].
Example:
An example of a quadratic equation that creates a parabola that looks like a smile is [tex] y=4x^2+8x+7[/tex].
The vertex of the parabola is at (-1,3) and the y-intercept is at (0,7).
