Find the value of b at which the graph of the function y = -x ^ + 2 bx + 3 passes through the point with coordinates (-1; 8)

1. If the graph of some function passes through some point, then the coordinates of this point must satisfy the equation of this graph.

2. Substitute the coordinates of the point A (-1; 8) into the given equation and find the value of the parameter b:

y = -x ^ 2 + bx + 3;

A (-1; 8); x0 = -1; y0 = 8;

8 = – (- 1) ^ 2 + b * (-1) + 3;

8 = -1 – b + 3;

8 = 2 – b;

b = 2-8;

b = -6.

The only value of the parameter at which the graph of the function passes through point A (-1; 8): b = -6.

Answer: b = -6.