To solve the equation x² = -x - 3 by graphing, we can plot the graphs of y = x² and y = -x - 3 on the same coordinate system and find their intersection points, which represent the solutions to the equation.
1. Graph y = x²:
- This is a parabolic function that opens upwards. The vertex of the parabola is at (0, 0).
- Plot the points (-1, 1), (1, 1), (2, 4), (-2, 4), and connect them to sketch the parabola.
2. Graph y = -x - 3:
- This is a linear function with a slope of -1 and y-intercept of -3.
- Plot the y-intercept at (0, -3) and find another point by moving down 1 unit and to the right 1 unit from the y-intercept. Connect these points to draw the line.
3. The solutions to the equation x² = -x - 3 are the x-coordinates of the points where the two graphs intersect.
4. Check the intersection points against the given options to determine the solutions:
- Potential solutions from the given options are x = -4, x = -3, and x = 1.
5. Confirm the correct solutions by looking at the intersection points of the graphs.
By following these steps, you can solve the equation x² = -x - 3 graphically and find the solutions that match the given options.
