The curve C has equation $y = x(5 - x)$ and the line L has equation $2y = 5x + 4$ - Edexcel - A-Level Maths Pure - Question 5 - 2012 - Paper 1

When sketching the graphs of C and L:

1. For Curve C ($y = x(5 - x)$):

   • The x-intercepts are at $(0,0)$ and $(5,0)$, found by setting $y = 0$: $x(5-x) = 0$
   • The y-intercept occurs when $x = 0$, giving the point $(0,0)$.

2. For Line L (y = rac{5}{2}x + 2):

   • The x-intercept occurs when $y = 0$. Solving: $$$$

ightarrow x = -rac{4}{5}$$

• The y-intercept occurs when $x = 0$, giving the point $(0,2)$.

3. When sketching:
   • Curve C is a downward-opening parabola with its vertex at $(2.5, 6.25)$ (calculated at $x = 2.5$).
   • Line L has a positive slope and passes through $(0, 2)$ and approximately $(1.6, 6)$.
   • Make sure to label the x-intercepts and y-intercepts of both curves clearly.