Yes.
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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.
You can easily identify the x-intercepts of a graph of a quadratic function by writing it as two binomial factors! Source: I am in Algebra 2 Honors!
The graph of a quadratic relation is a parobolic.
Yes. A quadratic function can have 0, 1, or 2 x-intercepts, and 0, 1, or 2 y-intercepts.
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.