Question 1086039
If they only intersect at one point then the line is tangent to the parabola at the intersection point.
Find the derivative of the parabola, the value of the derivative is equal to the slope of the tangent line at that point.
Find all values where
{{{dy/dx=m=6}}}
For the parabola,
{{{dy/dx=2x+2=6}}}
{{{2x=4}}}
{{{x=2}}}
So then find the value of the parabola when {{{x=2}}},
{{{y=x^2+2x+7}}}
{{{y=(2)^2+2(2)+7}}}
{{{y=4+4+7}}}
{{{y=15}}}
The line also intersects the parabola at this point, so then,
{{{6(2)+b=15}}}
{{{b=3}}}
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*[illustration 97.JPG].