Question

построить график функции y=2(x-2)^2. Указать при каких значениях переменной x функция возрастает или убывает

Answer 1

Ответ:

с 0 до 2 функция убывает, с 2 до 4 возрастает

Answer 2

Graph of the Function y=2(x-2)^2

To graph the function y=2(x-2)^2, we can start by identifying the key components of the function. The function is in the form of a quadratic function, which means it will have a parabolic shape. The general form of a quadratic function is y=a(x-h)^2+k, where (h,k) is the vertex of the parabola.

In the given function y=2(x-2)^2, the vertex is at the point (2, 0) and the coefficient of x^2 is positive, indicating that the parabola will open upwards.

Let's plot the graph of the function y=2(x-2)^2 to visualize its shape and behavior.

Increasing and Decreasing Intervals

To determine the intervals where the function y=2(x-2)^2 is increasing or decreasing, we can analyze the slope of the function. The function will be increasing where the slope is positive and decreasing where the slope is negative.

The slope of the function can be found by taking the derivative of the function and analyzing its sign.

Let's calculate the derivative of the function y=2(x-2)^2 and determine the intervals where the function is increasing or decreasing.

I'll now proceed to plot the graph of the function y=2(x-2)^2 and calculate the derivative to identify the intervals where the function is increasing or decreasing.