Question

Y=1.5x^2+6x-0.5 найдите наименьшее значение функции

Answer 1

Графиком этой квадратичной функции является парабола. наименьшего своего значения функция достигает в вершине параболы, поскольку старший коэффициент положителен, ветви направлены вверх.

х₀=-b/(2a)=-6/3=-2

y₀=y(-2)=1.5*4-12-0.5=-6.5

Ответ -6.5

Answer 2

To find the minimum value of the function, we need to determine the vertex of the parabola represented by the equation Y = 1.5x^2 + 6x - 0.5. The vertex of a parabola is the lowest point (minimum) if the parabola opens upward, as is the case here.

The x-coordinate of the vertex (let's call it "h") can be found using the formula: h = -b / (2a), where "a" is the coefficient of the x^2 term, and "b" is the coefficient of the x term.

In this case, a = 1.5 and b = 6:

h = -6 / (2 * 1.5) = -6 / 3 = -2

Now, to find the corresponding y-coordinate of the vertex (let's call it "k"), substitute the value of "h" back into the original equation:

k = 1.5 * (-2)^2 + 6 * (-2) - 0.5 k = 1.5 * 4 - 12 - 0.5 k = 6 - 12 - 0.5 k = -6.5

Therefore, the minimum value of the function is -6.5.