Please help me with this question: 

sketch the graph of the parabola y = 3(x - 2)² - 5 
I have tried everyway I can.

You must learn this rule:

The graph of y = a(x - h)² + k

is either a U-shaped graph or an inverted U-shaped graph.

The vertex (turning point is (h,k) and it goes through
(h-1,k+a) and (h+1),k+a)

Plot those three points and draw a U-shaped or inverted
U-shaped graph through those three points:

Using the rule on your equation:

y = 3(x - 2)² - 5

compare to

y = a(x - h)² + k

a = 3, h = 2, k = -5

The vertex (turning point is (h,k) = (2,-5) and it 
goes through (h-1,k+a) = (2-1,-5+3) = (1,-2),  and 
(2+1,-5+3) = (3,-2)

So plot those three points (1,-2), (2,-5) and (3,-2)

  

Now draw a smooth U-shaped graph through those three points:



Edwin