Question

Постройте график функции |x^2+2x-3|

Answer 1

Сначала строим график функции y=x^2+2x-3
x^2+2x-3=0;
D=16;
x1=1; (1;0)
x2=-3; (-3;0)
x=0; y=-3 (0;-3);
график - парабола
вершина: x=-2/2=-1; y=1-2-3=-4 (-1;-4)
нули: (1;0),(-3;0),(0;-3)
а>0 - ветви вверх;
строим график этой параболы,
и все что по оу меньше 0, симметрично отражаем относительно ох.
вот график:

Answer 2

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

To graph the function |x^2 + 2x - 3|, we need to plot the points that satisfy the equation and connect them to form a curve. Let's break down the process step by step:

1. Find the x-intercepts: To find the x-intercepts, we set the function equal to zero and solve for x. In this case, the function is |x^2 + 2x - 3|, so we have: |x^2 + 2x - 3| = 0

Solving this equation gives us two possible solutions for x: x = -3 and x = 1.

2. Find the y-intercept: To find the y-intercept, we substitute x = 0 into the function. In this case, we have: |0^2 + 2(0) - 3| = |-3| = 3

Therefore, the y-intercept is 3.

3. Plot the points: We have the x-intercepts at x = -3 and x = 1, and the y-intercept at y = 3. Let's plot these points on the graph.

4. Determine the behavior of the function: To determine the behavior of the function between the x-intercepts, we can analyze the sign of the expression inside the absolute value.

- When x < -3, the expression inside the absolute value becomes negative, so the function becomes -(x^2 + 2x - 3). - When -3 < x < 1, the expression inside the absolute value becomes positive, so the function becomes x^2 + 2x - 3. - When x > 1, the expression inside the absolute value becomes negative again, so the function becomes -(x^2 + 2x - 3).

This means that the graph will be reflected below the x-axis for x < -3 and x > 1, and above the x-axis for -3 < x < 1.

5. Connect the points: Using the information above, we can now connect the points and draw the graph of the function |x^2 + 2x - 3|.

Please note that without specific values for x, it is not possible to provide an accurate graph. However, the steps outlined above should help you understand how to graph the function |x^2 + 2x - 3|.

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