1. The problem is to find points on the graph of the function $$f(x) = \frac{1}{2}x^2 + \frac{3}{5}x + 7$$ and understand how to calculate the corresponding $y$ values for given $x$ values. 2. The formula for the function is given, and to find points $(x, y)$ on the graph, you substitute each $x$ value into the function and calculate $y = f(x)$. 3. Let's calculate $y$ for each $x$ value you provided: - For $x=2$: $$y = \frac{1}{2}(2)^2 + \frac{3}{5}(2) + 7 = \frac{1}{2} \times 4 + \frac{6}{5} + 7 = 2 + 1.2 + 7 = 10.2$$ - For $x=1$: $$y = \frac{1}{2}(1)^2 + \frac{3}{5}(1) + 7 = \frac{1}{2} + \frac{3}{5} + 7 = 0.5 + 0.6 + 7 = 8.1$$ - For $x=-1.5$: $$y = \frac{1}{2}(-1.5)^2 + \frac{3}{5}(-1.5) + 7 = \frac{1}{2} \times 2.25 - 0.9 + 7 = 1.125 - 0.9 + 7 = 7.225$$ - For $x=0$: $$y = \frac{1}{2}(0)^2 + \frac{3}{5}(0) + 7 = 0 + 0 + 7 = 7$$ - For $x=-1$: $$y = \frac{1}{2}(-1)^2 + \frac{3}{5}(-1) + 7 = \frac{1}{2} - 0.6 + 7 = 0.5 - 0.6 + 7 = 6.9$$ - For $x=-2$: $$y = \frac{1}{2}(-2)^2 + \frac{3}{5}(-2) + 7 = \frac{1}{2} \times 4 - 1.2 + 7 = 2 - 1.2 + 7 = 7.8$$ 4. So the points on the graph are: $$(2, 10.2), (1, 8.1), (-1.5, 7.225), (0, 7), (-1, 6.9), (-2, 7.8)$$ 5. The key is to substitute each $x$ value into the function and carefully perform the arithmetic to find $y$. Your work with $x = -\frac{3}{2(1)}$ seems to be related to finding the vertex or critical point, but for plotting points, just substitute $x$ values directly. 6. If you want, I can help explain how to find the vertex or other features of the parabola next.