Question

При каких значениях х функция y=-3x^2+6x-5 принимает неотрицательные значения

Answer 1

Производная y

у = -6х+6=0

х=1

у=-3+6-5=-2

значит при любых х,у будет принимать отрицательные значения,простой график для наглядности

 

Answer 2

Finding Non-Negative Values of y for y = -3x^2 + 6x - 5

To find the values of x for which the function y = -3x^2 + 6x - 5 takes non-negative values, we need to determine the range of x that satisfies this condition.

The function y = -3x^2 + 6x - 5 is a quadratic function, and its graph is a parabola. The vertex of the parabola represents the minimum or maximum point of the function, and the parabola opens downwards because the coefficient of x^2 is negative.

To find the values of x for which the function y is non-negative, we need to find the x-values where the function crosses or touches the x-axis, as these are the points where y = 0 or y is non-negative.

The x-values where the function crosses or touches the x-axis can be found using the quadratic formula:

Quadratic Formula: The solutions to the quadratic equation ax^2 + bx + c = 0 are given by: \[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}\]

In this case, the quadratic equation is -3x^2 + 6x - 5 = 0, and we can use the quadratic formula to find the x-values.

Applying the Quadratic Formula

Using the quadratic formula, we can find the x-values where the function y = -3x^2 + 6x - 5 crosses or touches the x-axis.

The quadratic formula gives the solutions for x as: \[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}\]

For the given function -3x^2 + 6x - 5, the coefficients are: - a = -3 - b = 6 - c = -5

Substituting these values into the quadratic formula, we get: \[x = \frac{{-6 \pm \sqrt{{6^2 - 4(-3)(-5)}}}}{{2(-3)}}\]

Solving for x, we get the x-values where the function crosses or touches the x-axis.

Conclusion

By solving the quadratic equation -3x^2 + 6x - 5 = 0 using the quadratic formula, we can find the x-values where the function y = -3x^2 + 6x - 5 takes non-negative values.