1. **State the problem:** We are given the function $$y = 0.9x + \frac{x^2}{15}$$ and asked to draw its graph for $$0 \leq x \leq 35$$ where $$x$$ represents speed (in m/s) and $$y$$ represents stopping distance (in metres). 2. **Understand the function:** The function is a quadratic with a linear term and a quadratic term. The quadratic term $$\frac{x^2}{15}$$ makes the graph a parabola opening upwards. 3. **Calculate some points:** - At $$x=0$$: $$y = 0.9(0) + \frac{0^2}{15} = 0$$ - At $$x=20$$: $$y = 0.9(20) + \frac{20^2}{15} = 18 + \frac{400}{15} = 18 + 26.67 = 44.67$$ - At $$x=35$$: $$y = 0.9(35) + \frac{35^2}{15} = 31.5 + \frac{1225}{15} = 31.5 + 81.67 = 113.17$$ 4. **Plotting the graph:** The graph starts at the origin (0,0), rises slowly at first due to the linear term, then more steeply because of the quadratic term. 5. **Summary:** The graph is a parabola-like curve starting at (0,0) and increasing to about (35,113.17) on the stopping distance axis.