Calculus slope question

Question

A curse has a slope of 4x+2. What is the equation of the curve if it passes through the point (1,8)? Does this just mean to find the equation of the tangent line? 

Answer 1

The equation of the slope of a point on a curve is the first derivative of the equation for the curve.

 

f'(x) = 4x + 2

f(x) = 2x² + 2x + c

 

8 = 2(1)² + 2(1) + c

8 = 2 + 2 + c

4 = c

 

f(x) = 2x² + 2x + 4