The diagram shows part of the graph of y = x^2 - 2x + 3 (a) By drawing a suitable straight line, use your graph to find estimates for the solutions of x^2 - 3x - 1 = 0 (b) Calculate an estimate for the gradient of the graph at the point P - Edexcel - GCSE Maths - Question 20 - 2017 - Paper 2

To estimate the gradient at the point P where $x=2$, I first find the coordinates of point P from the graph. The corresponding y-coordinate when substituting $x=2$ into the function $y = x^2 - 2x + 3$ is calculated as follows:

$y = 2^2 - 2(2) + 3 = 4 - 4 + 3 = 3$

Thus, the point P is (2, 3). The next step is to determine the gradient by finding the slope of the tangent at point (2, 3). The derivative of the function

$f'(x) = 2x - 2$

Substituting $x = 2$ calculates the gradient:

$f'(2) = 2(2) - 2 = 4 - 2 = 2$

Therefore, I estimate the gradient at point P to be approximately $2$.