Intersection of a line and a curve.

Equating the two equations doesn't mean the curve and the line share a single value of $y$; it means that you're assuming they share a value of $y$, and then getting an equation for the corresponding shared value of $x$. This says nothing about how many shared pairs $(x, y)$ there might be.


What is an intersection?

An intersection is where both $y$ for each function are equal for the same $x$.

Consider $f(x)=g(x)$.

Your intersection(s) are ALL the points where you can plug (the same) $x$ into both $f(x)$ and $g(x)$ and get an equality.

Because $f(x)=g(x)$, $y=y$, if that makes sense.

And this can happen say $0,1,2...\infty$ times.

Tags:

Linear Algebra

Algebra Precalculus

Quadratics

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