Question

In the xy-plane, the line y=x+k, where k is constant, is tangent to the graph of y=x^2-3x+1. What is the value of k?

Answer 1

differentiate \[y=x^2-3x+1\] then set the slope of the tangent line equal to 1to get the x coordinate of the point where y=x+k is tangent to \[y=x^2-3x+1\], then plug back into the quadratic to get the y coordinate and then plug them into y=x+k to find k