The graph of a quadratic relation is a parobolic.
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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.
Yes.
In general, quadratic equations have graphs that are parabolas. The quadratic formula tells us how to find the roots of a quadratic equations. If those roots are real, they are the x intercepts of the parabola.
The derivative of a quadratic function is always linear (e.g. the rate of change of a quadratic increases or decreases linearly).
They will be on the horizontal x axis of the graph (look for the x-intercepts).