Question

200б тому кто первый мне поможет решить Х^2 + 6х + 32 при каком значении х выражение принимает наименьшое значение

Answer 1

Y=x^2+6X+7  - парабола, ищем минимум
первая производная : 2*Х+6=0 --->  X(min)=-3
При X= -3 данное выражение имеет минимальное значение, равное
9-18+32=23

Answer 2

Finding the Minimum Value of the Expression

To find the minimum value of the expression x^2 + 6x + 32, we can use the formula for the vertex of a parabola, which is given by (-b/2a, c - b^2/4a), where a is the coefficient of x^2, b is the coefficient of x, and c is the constant term.

Calculating the Minimum Value

In this case, the expression is x^2 + 6x + 32, so: - a = 1 - b = 6 - c = 32

Using the formula, the x-coordinate of the vertex is -b/2a and the y-coordinate is c - b^2/4a.

Substituting the values: - x-coordinate of the vertex = -6 / (2*1) = -3 - y-coordinate of the vertex = 32 - 6^2 / (4*1) = 32 - 36 / 4 = 32 - 9 = 23

So, the expression x^2 + 6x + 32 takes its minimum value of 23 when x = -3.