The graph of the function y = x ^ 2 + bx + 3 passes through the point A (-4; 51). Find the coefficient b.

In order to find the value of the coefficient b for the function y = x ^ 2 + bx + 3, which passes through the point A (-4; 51), you need to substitute the number (-4) instead of the variable x, and substitute the number 51 instead of the variable y Next, solve the resulting equation. Therefore, we get:

51 = (-4) ^ 2 + b * (-4) + 3 (simplify the right side of the equation);

51 = 16 – 4b + 3 (we will give similar terms on the right side);

51 = 16 + 3 – 4b;

51 = 19 – 4b;

4b = 19-51;

4b = -32 (in order to find an unknown factor, you need to divide the product by a known factor);

b = -32: 4;

b = -8.

Answer: -8.