At what point is the tangent drawn to the graph of the function y = x ^ 2-2x + 1 parallel to the straight line y = -4x-4?

The slope of the tangent line given by the equation y = – 4 * x – 4 is equal to – 4, since the derivative of the function y = k * x + b is equal to k.

Find the derivative of the parabola and equate its value with the obtained value of the slope.

The derivative of y = x ^ 2 – 2 * x + 1 is equal to y = 2 * x – 2.

– 4 = 2 * x – 2.

Find x: 2 * x = – 4 + 2; 2 * x = – 2; x = – 2/2; x = – 1.

Let’s find the paired coordinate y and get the answer: y = 1 + 2 + 1; y = 4.

Answer: the derivative y = x ^ 2 – 2 * x + 1 is parallel to the graph of the function y = – 4 * x – 4 at the point with coordinates x = – 1 y = 4.