To solve the equation x² + 2x – 6 = 2x + 3, we first simplify the equation. We can start by eliminating the 2x from both sides:
x² + 2x – 6 – 2x = 3
This simplifies to:
x² – 6 = 3
Next, we can move the 3 from the right side to the left side:
x² – 6 – 3 = 0
This gives us:
x² – 9 = 0
Now, we can factor this equation:
(x – 3)(x + 3) = 0
Setting each factor equal to zero gives us the potential solutions:
- x – 3 = 0 ⟹ x = 3
- x + 3 = 0 ⟹ x = -3
Thus, the solutions to the equation are x = 3 and x = -3. Now, when looking at the graphs provided, you need to identify which one correctly shows these solutions as the x-intercepts (where the graph crosses the x-axis).
The graph will typically appear as a parabola opening upwards, crossing the x-axis at -3 and 3. If you can analyze the graphs based on these intersections, you should be able to select the correct one. Remember to look carefully! The right graph should display both points accurately along the x-axis, demonstrating the correct solutions for the equation.
In conclusion, to answer your question, the correct graph is the one that shows x-intercepts at x = -3 and x = 3.