Question

Наименьшее значение функции y=x²+6x+c равно -2. Найти c

Answer 1

Графиком функции является парабола ветвями вверх ⇒ наименьшее значение это её вершина по Oy

Чтобы найти координату по Ox воспользуемся формулой x₀=(-b/2а)=(-6/2)=(-3)

Координата по Oy известна и равна -2

Подставим всё известное в уравнение

(-3)²+6*(-3)+с=(-2)

9-18+с=-2

с=7

Ответ 7.

Answer 2

To find the value of c, we are given that the minimum value of the function y = x² + 6x + c is equal to -2. The minimum value of a quadratic function in the form of ax² + bx + c occurs at the vertex of the parabola. The x-coordinate of the vertex is given by -b / 2a.

In this case, a = 1 (coefficient of x²) and b = 6 (coefficient of x). So, the x-coordinate of the vertex is:

x-coordinate of vertex = -b / 2a = -6 / (2 * 1) = -6 / 2 = -3

Now, to find the corresponding y-coordinate (which is the minimum value of the function), we substitute the x-coordinate back into the function:

y = (-3)² + 6(-3) + c y = 9 - 18 + c y = -9 + c

Since the minimum value of the function is given as -2, we have:

-9 + c = -2

To find c, isolate it on one side of the equation:

c = -2 + 9 c = 7

So, the value of c is 7.