Question

У=х^2+2|х|-3постройте график

Answer 1

Вот  график   у = х^2+2*х-3

Answer 2

Graph of the Function y = x^2 + 2|x| - 3

To graph the function y = x^2 + 2|x| - 3, we can start by analyzing the different parts of the equation.

The term x^2 represents a parabolic curve that opens upwards. The term 2|x| represents a V-shaped curve with its vertex at the origin. The term -3 represents a horizontal shift downwards by 3 units.

Combining these components, we can plot the graph of the function.

Steps to Plot the Graph:

1. Determine the key points: - The vertex of the parabolic curve is at (0, -3). - The vertex of the V-shaped curve is at (0, 0).

2. Plot the vertex points: - Plot the point (0, -3) as the vertex of the parabolic curve. - Plot the point (0, 0) as the vertex of the V-shaped curve.

3. Determine the x-intercepts: - To find the x-intercepts, set y = 0 and solve for x. - For the parabolic curve, solve x^2 + 2|x| - 3 = 0. - For the V-shaped curve, solve 2|x| - 3 = 0.

4. Determine the y-intercept: - To find the y-intercept, set x = 0 and solve for y.

5. Plot additional points: - Choose a few x-values on either side of the x-intercepts and calculate the corresponding y-values. - Plot these points on the graph.

6. Connect the points: - Use a smooth curve to connect the plotted points, taking into account the shape of the parabolic and V-shaped curves.

Graph of y = x^2 + 2|x| - 3:

The graph of the function y = x^2 + 2|x| - 3 is shown below:


Please note that the graph is a visual representation and may not be to scale. It is always recommended to use graphing software or a graphing calculator for accurate and precise graphs.

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