Subjects algebra

Parabola Reflection D67E33

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Search Solutions

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.