Question 1114498
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What is meant by 'tangent to the parabola'? 
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The line which touches but does not cross the parabola at the particular local point.


{{{y = x^2-x-12}}}
-
{{{dx/dy=2x-1}}}

Slope of a tangent line to the parabola is  {{{2x-1}}}.


{{{y=mx+c=(2x-1)x+c=1*x+c}}}
meaning, {{{2x-1=1}}}
{{{2x=2}}}
{{{x=1}}}


The point on the parabola for x=1 is
{{{y=x^2-x-12}}}
{{{y=1-1-12}}}
{{{y=-12}}}



This point (1,-12) is both on the parabola and also on the line {{{y=x+c}}}.

{{{c=y-x}}}
{{{c=-12-1}}}
{{{highlight(c=-13)}}}



The tangent line at that point:
{{{highlight(y=x-13)}}}

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{{{graph(300,300,-7,7,-13,1,x^2-x-12,x-13)}}}