The curve C has equation $y = x(5 - x)$ and the line L has equation $2y = 5x + 4$ (a) Use algebra to show that C and L do not intersect - Edexcel - A-Level Maths Pure - Question 7 - 2012 - Paper 1

In the sketch, we will display both curves:

• Curve C:

  • It has a parabolic shape opening downwards.
  • It passes through the points (0, 0) and (5, 0).
  • The y-intercept is at (0, 0), and the vertex can be found at (2.5, 6.25) using the vertex formula.

• Line L:

  • It is a straight line with a positive gradient.
  • It intersects the y-axis at (0, 2).
  • The x-intercept can be found by setting $y=0$, leading to $5x + 4 = 0 \Rightarrow x = -\frac{4}{5}$. This is approximately (-0.8, 0).

Both curves should be clearly labeled, including their respective axis intersection points.