At what values of the coefficients b and c point A (-7; 49) is the vertex of the parabola given by the equation y = x^2 + bx + c.

The abscissa of the vertex A (x0, y0) of the parabola:

y = a * x ^ 2 + b * x + c;

calculated by the formula:

x0 = – b / (2a);

To determine the ordinate y0, it is necessary to substitute x0 into the original equation of the parabola:

y0 = a * (x0) ^ 2 + b * (x0) + c;

In our case, the vertex A has coordinates (-7; 49) and:

y = x ^ 2 + b * x + c;

x0 = – b / 2 = -7;

y0 = (- b / 2) ^ 2 + b * (- b / 2) + c = – b ^ 2/4 + c = 49;

We get:

b = (-7) * (-2) = 14;

c = 49 + 14 ^ 2/4 = 98.

Answer: b = 14; c = 98.