I assume this question refers to the coefficient of the squared term in a quadratic and not a variable (as stated in the question). That is, it refers to the a in ax2 + bx + c where x is the variable.
When a is a very large positive number, the graph is a very narrow or steep-sided cup shape. As a become smaller, the graph gets wider until, when a equals zero (and the equation is no longer a quadratic) the graph is a horizontal line. Then as a becomes negative, the graph becomes cap shaped. As the magnitude of a increases, the sides of the graph become steeper.
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The zeros of a quadratic function, if they exist, are the values of the variable at which the graph crosses the horizontal axis.
The graph of a quadratic relation is a parobolic.
The wording is confusing, as a quadratic function is normally a function of one variable. If you mean the graph of y = f(x) where f is a quadratic function, then changes to the variable y will do some of those things. The transformation y --> -y will reflect the graph about the x-axis. The transformation y --> Ay (where A is real number) will cause the graph to stretch or shrink vertically. The transformation y --> y+A will translate it up or down.
On a line graph, where is the dependent variable placed?
Yes.