Question

Постройте график функции y=x*|x|-x-12

Answer 1

F(x)=x*|x|-x-12
Таблица и график во вложении

Answer 2

Graph of the Function y=x*|x|-x-12

To graph the function y=x*|x|-x-12, we can start by understanding the behavior of the absolute value function and then apply it to the given function.

The absolute value function |x| is defined as: - |x| = x, if x >= 0 - |x| = -x, if x < 0

Let's break down the given function and then plot its graph.

The function y=x*|x|-x-12 can be rewritten as: - y = x^2 - x - 12, if x >= 0 - y = -x^2 - x - 12, if x < 0

Now, let's plot the graph of the function y=x^2-x-12 and y=-x^2-x-12 separately and then combine them to get the graph of the original function.

Graph of y=x^2-x-12 (for x >= 0)

This is a quadratic function with a positive coefficient for x^2. It represents an upward-opening parabola.
The vertex of the parabola can be found using the formula: x = -b/(2a), where a is the coefficient of x^2 and b is the coefficient of x.
The x-coordinate of the vertex is x = -(-1)/(2*1) = 1/2.
Substitute x = 1/2 into the function to find the y-coordinate of the vertex.

Graph of y=-x^2-x-12 (for x < 0)

This is a quadratic function with a negative coefficient for x^2. It represents a downward-opening parabola.
The vertex of the parabola can be found using the formula: x = -b/(2a), where a is the coefficient of x^2 and b is the coefficient of x.
The x-coordinate of the vertex is x = -(-1)/(2*(-1)) = 1/2.
Substitute x = 1/2 into the function to find the y-coordinate of the vertex.

Combined Graph

Plot the graphs of y=x^2-x-12 and y=-x^2-x-12 on the same coordinate system to get the graph of the original function y=x*|x|-x-12.

The resulting graph will show the behavior of the given function for both positive and negative values of x.

I hope this helps! Let me know if you need further assistance.