The equation presented in your screenshot is:

$x^2 + 6x - 6 = -3x^2 - 2x + 11$

To solve this algebraically:

1. Move all terms to one side of the equation: $x^2 + 6x - 6 + 3x^2 + 2x - 11 = 0$ Combine like terms: $4x^2 + 8x - 17 = 0$

2. This is a quadratic equation of the form: $4x^2 + 8x - 17 = 0$

Solving using the quadratic formula:

The quadratic formula is given by: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ where $a = 4$, $b = 8$, and $c = -17$.

Let's plug in these values to calculate the solutions.The solutions to the equation $4x^2 + 8x - 17 = 0$ are approximately:

$x_1 \approx 1.29 \quad \text{and} \quad x_2 \approx -3.29$

These values represent the x-intercepts where the quadratic equation equals zero.

Now, looking at the graphs in your screenshot, the correct graph should intersect the x-axis at points approximately near $x = 1.29$ and $x = -3.29$. Based on this, Graph D seems to be the correct choice.

Would you like further details on how the graph looks or how to confirm this visually?

Here are 5 related questions you might consider:

1. How do you graph quadratic functions using the vertex and intercepts?
2. What is the significance of the discriminant in the quadratic formula?
3. How would this equation be solved if the discriminant were negative?
4. Can this equation be factored instead of using the quadratic formula?
5. How does changing the coefficients in a quadratic equation affect the graph's shape?

Tip: Always check the discriminant first to determine whether the solutions will be real or complex before using the quadratic formula!