Parabola Reflection D67E33
1. The problem asks for the graph of the reflection of the parabola given by the equation $$y = x^2 + 3x - 10$$ over the y-axis.
2. Reflecting a graph over the y-axis means replacing every $x$ with $-x$ in the equation.
3. Start with the original equation:
$$y = x^2 + 3x - 10$$
4. Replace $x$ by $-x$:
$$y = (-x)^2 + 3(-x) - 10$$
5. Simplify the expression:
$$y = x^2 - 3x - 10$$
6. The reflected parabola has the equation:
$$y = x^2 - 3x - 10$$
7. This parabola opens upward (since the coefficient of $x^2$ is positive), has a vertex below the x-axis, and is shifted to the left compared to the original parabola.
8. Among the given options, Graph D matches this description: a parabola opening upward with vertex below the x-axis, shifted to the left on the x-axis.
**Final answer:** The graph of the reflection over the y-axis is Graph D.