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\noindent {\bf Problem statement} Sketch the parabola $y = x^2$ and
the line $y = 2x - 1$.

\medskip

\noindent a) Show that $(1,1)$ is the only point where the parabola
and line intersect.

\medskip

\noindent b) Show that any line other than $y=2x-1$ which contains
$(1,1)$ must intersect the parabola in some point besides $(1,1)$.

\smallskip

\noindent {\bf Suggestion}  What condition guarantees that the line
$y = mx + b$ contains the point  $(1,1)$? What condition
guarantees that the quadratic equation $x^2 = mx + b$ has only
one root?

%contributed by Michael O'Nan







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