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Q: What do all graphs of quadratic functions have in common?

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All quadratic functions with real coefficients can be graphed on a standard x-y graph. Not all quadratic functions have real roots, maybe that's what you were thinking of?

Where they all intersect.

All you do is set the quadratic function to equal to 0. Then you can either factor or use the quadratic formula to solve for your unknown variable.

They are all represented by straight lines.

All direct variation graphs are linear and they all go through the origin.

Polynomials have graphs that look like graphs of their leading terms because all other changes to polynomial functions only cause transformations of the leading term's graph.

It is not. If f(x) = ax2 and g(x) = -ax2 then the separate graphs will be two quadratic curves, f being "happy" and g being "sad". But f(x) + g(x) = 0 for all x and so is the x axis, not a quadratic.

No, sometimes the entire graph is completely above (or completely below) the x axis.

All graphs are graphical graphs because if they were not graphical graphs they would not be graphs!

There are 2 main functions that all dictionaries have in common. These dictionaries define words and tell the user how to use them.

Anything involving a square law automatically invokes a quadratic function by definition, even if the equations is as simple as y = x^2, such as the area of a square (hence the names). At a more advanced level, quadratic and higher-order functions crop up in all manner of real-life science and engineering problems.

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