Here is the graph of $y = -x^2 - 6x + 4$ - Edexcel - GCSE Maths - Question 7 - 2022 - Paper 2

The turning point (vertex) of a quadratic equation in the form $y = ax^2 + bx + c$ can be found using the formula:

$x = -\frac{b}{2a}.$

Here, $a = -1$ and $b = -6$.

Substituting these values gives:

$x = -\frac{-6}{2(-1)} = \frac{6}{-2} = -3.$

To find the y-coordinate, substitute $x = -3$ back into the equation:

$y = -(-3)^2 - 6(-3) + 4 = -9 + 18 + 4 = 13.$

Therefore, the coordinates of the turning point are (-3, 13).

From the graph, we can visually estimate the roots where the curve intersects the x-axis. Observing the graph, the roots occur approximately between:

1. $x \approx -4$
2. $x \approx -1$

Thus, the estimated roots of the equation $-x^2 - 6x + 4 = 0$ are around $x = -4$ and $x = -1$.