The point of tangency between the line y = 2x - 1 and the parabola y = x^2 is found by setting the two equations equal and solving for x. The solution is x = 1, and after substituting x back into the original equation, we find that the point of tangency is (1, 1).
To find the point of tangency between the line y = 2x - 1 and the parabola y = x^2, we should equate these two equations and solve for x, because at the point of tangency, both the y values and slopes of the line and the curve will be the same.
First, we set the two equations equal to each other to find the x coordinate of the tangency point:
2x - 1 = x^2
Rearrange the equation:
x^2 - 2x + 1 = 0
This is a quadratic equation that factors to:
(x - 1)(x - 1) = 0
Therefore, x = 1 is the solution. To find the y coordinate, we substitute x back into either original equation. Using the linear equation:
y = 2(1) - 1
y = 1
The point of tangency is (1, 1).