A quadratic function can be written y=ax^2+bx+c, the standard U-shaped ot inverted U-shaped parabola. x=dy^2+ey+f is a standard parabola lying on its side.
The coefficient a or d affects the width and direction of the parabola. If a is negative the U is inverted; if d is negative the arms of the U extend to the left (negative). As a or d get larger the parabola becomes narrower.
The equation of the parabola can also be written y-k=a(x-h)^2. This produces y=ax^2-2xah+ah^2+k. In this presentation, b is replaced by -2ah and c by ah^2+k. (h,k) is the vertex or origin of the parabola, the minimum or maximum point of the curve, depending on whether we have a U-shaped (a is positive) or inverted U (a is negative). So h and k represent the horizontal and vertical displacement of the parabola. Similar displacements apply to the sideways parabola.
So you can see the effect of changing the coefficients and constant of a quadratic, which is in effect the equation of a parabola.