Figure 1 shows a sketch of a curve C with equation $y = f(x)$ and a straight line l - Edexcel - A-Level Maths Pure - Question 9 - 2020 - Paper 1

Knowing that $f(x)$ is a quadratic function with a minimum turning point at $(-2, 13)$, we express it in vertex form:

$f(x) = a(x + 2)^2 + 13$

To find the value of $a$, we can use the other point $(0, 25)$:

$25 = a(0 + 2)^2 + 13 \Rightarrow 25 = 4a + 13 \Rightarrow 4a = 12 \Rightarrow a = 3$

Thus, the equation of the curve is:

$f(x) = 3(x + 2)^2 + 13$

The shaded region R is defined as follows:

$R = \{(x,y) : f(x) \geq y \text{ and } y \leq 6x + 25, \text{ for } -2 \leq x \leq 0 \}$

This encompasses the area between the curve C and the line l over the specified interval.