Final answer:
The point at which the curve y=x^2-4x+3 has gradient -2 is (1, 0).
Step-by-step explanation:
To find the point at which the curve y = x² - 4x + 3 has a gradient of -2, we need to find the x-coordinate of the point where the derivative of the curve is -2. The derivative of the curve is given by the equation y' = 2x - 4. Setting the derivative equal to -2 and solving for x, we get:
2x - 4 = -2
2x = 2
x = 1
So, the x-coordinate of the point is 1. To find the y-coordinate, we substitute the value of x into the original equation:
y = (1)² - 4(1) + 3
y = 1 - 4 + 3
y = 0
Therefore, the point at which the curve has a gradient of -2 is (1, 0).