1. **State the problem:** We need to match each quadratic function to its corresponding graph. 2. **Recall the general form of a quadratic function:** $$f(x) = ax^2 + bx + c$$ where $a$ determines the direction of the parabola (upward if $a>0$, downward if $a<0$), and $c$ is the y-intercept. 3. **Analyze each function:** - For $$f(x) = 2x^2$$, the coefficient $a=2$ is positive, so the parabola opens upward. The vertex is at $(0,0)$ since there is no $bx$ or $c$ term. - For $$g(x) = -x^2 - 1$$, the coefficient $a=-1$ is negative, so the parabola opens downward. The vertex is at $(0,-1)$. 4. **Match to graphs:** - The left graph is a downward-opening parabola with vertex at $(0,-1)$, so it matches $$g(x) = -x^2 - 1$$. - The right graph is an upward-opening parabola with vertex at $(0,0)$, so it matches $$f(x) = 2x^2$$. **Final answer:** - Left graph: $$g(x) = -x^2 - 1$$ - Right graph: $$f(x) = 2x^2$$