1. **Problem Statement:** Determine which statement about the graph of $$y = (3 - 2x)^2 + 1$$ is true. 2. **Rewrite the function:** Expand the square to get the quadratic in standard form. $$y = (3 - 2x)^2 + 1 = (3 - 2x)(3 - 2x) + 1 = 9 - 12x + 4x^2 + 1$$ 3. **Simplify:** $$y = 4x^2 - 12x + 10$$ 4. **Check the given options:** - Option A: "The graph cuts the x-axis." To check if the graph cuts the x-axis, solve $$y=0$$: $$4x^2 - 12x + 10 = 0$$ Calculate the discriminant $$\Delta$$: $$\Delta = (-12)^2 - 4 \times 4 \times 10 = 144 - 160 = -16$$ Since $$\Delta < 0$$, no real roots exist, so the graph does **not** cut the x-axis. - Option B: "The graph opens downwards." The coefficient of $$x^2$$ is $$4 > 0$$, so the parabola opens **upwards**, not downwards. - Option C: "The axis of symmetry is $$x = 1.5$$." The axis of symmetry for $$y = ax^2 + bx + c$$ is $$x = -\frac{b}{2a}$$. Here, $$a=4$$ and $$b=-12$$, so: $$x = -\frac{-12}{2 \times 4} = \frac{12}{8} = 1.5$$ This matches the option. - Option D: "The y-intercept of the graph is 1." The y-intercept is the value of $$y$$ when $$x=0$$: $$y = 4(0)^2 - 12(0) + 10 = 10$$ So the y-intercept is 10, not 1. 5. **Conclusion:** The correct statement is **C. The axis of symmetry is $$x = 1.5$$**. Final answer: **C**