A parabola can be written in the form [tex] y = ax^{2} + bx + c[/tex]. If x is squared then the parabola open vertically (either upwards or downwards) while if y is squared then the parabola opens horizontally to the left or right.
since in this equation x is squared the the parabola opens either upwards or downwards vertically.
If the coefficient a is positive, then that means that the parabola has a minimum value and opens upwards (smiley face) while if a is negative then that means the parabola has a maximum and opens downwards (sad face)
since in this equation a is positive then that means that not only does the parabola open on the vertical plane, but it also has a minimum and opens upwards (smiley face).
