Question

Построй график функции y=|x|(x+2)-5x

Answer 1

Y=|x|(x+2)-5x_______

Answer 2

Plot of the Function y = |x|(x+2)-5x

To plot the function y = |x|(x+2)-5x, we can start by analyzing the equation and identifying key points and characteristics.

The function y = |x|(x+2)-5x can be broken down into two parts: |x| and (x+2)-5x. Let's analyze each part separately:

1. |x|: The absolute value function |x| takes the input x and returns its absolute value, which means it always returns a non-negative value. For x ≥ 0, |x| = x, and for x < 0, |x| = -x.

2. (x+2)-5x: This part of the equation involves a combination of addition and subtraction. Simplifying it, we get (x+2)-5x = x + 2 - 5x = -4x + 2.

Now that we have simplified the equation, we can plot the function.

Plotting the Function

To plot the function y = |x|(x+2)-5x, we need to consider different intervals for x and calculate the corresponding values of y.

1. For x < 0: - Since x is negative, |x| = -x. - Substituting this into the equation, we get y = -x(-4x + 2) = 4x^2 - 2x. - We can calculate the values of y for different x values in this interval.

2. For x ≥ 0: - Since x is non-negative, |x| = x. - Substituting this into the equation, we get y = x(-4x + 2) = -4x^2 + 2x. - We can calculate the values of y for different x values in this interval.

By calculating the values of y for different x values in the given intervals, we can plot the graph of the function y = |x|(x+2)-5x.

Note: Since we don't have specific x values or a range mentioned in the question, we will provide a general overview of the graph based on the equation.

Graphical Overview

The graph of the function y = |x|(x+2)-5x will have different shapes in different intervals of x. Here is a general overview of the graph:

1. For x < 0: - The graph will be a downward-opening parabola with its vertex at the origin (0, 0). - As x decreases, the value of y will increase.

2. For x ≥ 0: - The graph will be an upward-opening parabola with its vertex at the origin (0, 0). - As x increases, the value of y will decrease.

Please note that without specific x values or a range, we cannot provide an accurate and detailed graph. However, the general overview mentioned above should give you an idea of the shape and behavior of the graph.

I hope this helps! Let me know if you have any further questions.