Question

Найдите область значений функции y= -x²+6x-5

Answer 1

X=R Y=R. Так как мы можем поставить любой действительной число У тоже может быть +инфинити -инфинити

Answer 2

Finding the Range of the Function y = -x² + 6x - 5

To find the range of the function y = -x² + 6x - 5, we can use the properties of quadratic functions to determine the maximum or minimum value of the function. The range of the function will then be determined by this extreme value.

Using the Given Function

The given function is y = -x² + 6x - 5.

Finding the Extreme Value

To find the extreme value of the function, we can use the formula for the x-coordinate of the vertex of a quadratic function, which is given by x = -b/2a. In this case, the coefficient of x² is -1 (a) and the coefficient of x is 6 (b).

Using the formula, we get: x = -6 / (2 * (-1)) = -6 / -2 = 3

Calculating the Corresponding y-Value

Substitute the x-value into the original function to find the corresponding y-value: y = -(3)² + 6(3) - 5 = -9 + 18 - 5 = 4

Conclusion

Therefore, the range of the function y = -x² + 6x - 5 is y ≤ 4. This means that the function has a maximum value of 4, and all other y-values will be less than or equal to 4.

This conclusion is based on the properties of quadratic functions and the calculation of the extreme value of the given function.

If you have any further questions or need additional assistance, feel free to ask!