Can AnyOne Try to Explain This Real Quick Please

[Guest]

Find the equation of the line tangent to the graph y=2x^2-3x+1 at the point where x=2. Write your answer in slope intercept form: y=mx+k.

 

[Gene]

It is best if you show your work so we know where to help.
y=2x^2-3x+1
Find dy/dx
y'=4x-3
Solve at x=2
y(2)=3
Solve at x=2
y'(2)=5 = m

y=mx+k
3=5*2+k=10+k
k=-7