1. The problem asks to translate the graph of a parabola 3 units to the left using a table of points. 2. The original parabola has vertex at approximately $(3, -4)$ and x-intercepts at approximately $(1, 0)$ and $(5, 0)$. 3. To translate a graph 3 units to the left, we subtract 3 from each $x$-coordinate of the points on the graph. 4. Let the original points be $P = (x, y)$. The translated points $P'$ will be: $$P' = (x - 3, y)$$ 5. Using the key points: - Vertex: $(3, -4) \to (3 - 3, -4) = (0, -4)$ - Left x-intercept: $(1, 0) \to (1 - 3, 0) = (-2, 0)$ - Right x-intercept: $(5, 0) \to (5 - 3, 0) = (2, 0)$ 6. Constructing the table: | Original $(x, y)$ | Translated $(x - 3, y)$ | |-------------------|-------------------------| | $(1, 0)$ | $(-2, 0)$ | | $(3, -4)$ | $(0, -4)$ | | $(5, 0)$ | $(2, 0)$ | 7. This translation shifts the entire parabola 3 units left, moving the vertex and intercepts accordingly. Final answer: The translated points are $(-2, 0)$, $(0, -4)$, and $(2, 0)$.