At what value of the coefficients b and c point A (-7; 49) is the vertex

At what value 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? 1) b = 14, c = 982) b = -14, c = -983 ) b = 7, c = -49

We have the equation of the function:

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

The function is quadratic, the graph is a parabola.

Let’s find the derivative of the function:

y ‘= 2 * x + b;

Find the critical point:

2 * x = -b;

x = -b / 2 – critical point (minimum point, to be more precise).

Substitute the value of the abscissa of the vertex of the parabola into the formula:

-7 = -b / 2;

b = 14;

We find the value of the parameter c – we substitute all known quantities into the function formula:

49 = 49 – 14 * 7 + s;

c = 98;

y = x ^ 2 + 14 * x + 98 is the equation of our parabola.