What are the coordinates of the vertex of the parabola $y = - 2 (x - 2)^{2} - 5$ ?

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A particle moves along a line with displacement $x = t^{3} - 6 t^{2} + 9 t$ metres at time $t$ seconds. At what time $t > 0$ is the particle first…
Solve $lo g_{2} x + lo g_{2} (x - 2) = 3$ for $x$ .
What is the area enclosed between the curve $y = x^{2}$ and the line $y = x$ ?
For events $A$ and $B$ , $P (B) = 0.3$ and $P (A \cap B) = 0.075$ . What is $P (A ∣ B)$ ?
If $f (x) = (5 x + 4)^{4}$ , find $f^{'} (2)$ .
Find the $x$ -coordinate of the local minimum of $f (x) = x^{3} - 27 x$ .