book Maths Puzzle Numerical Ability

I don't understand how this problem was worked out? f(x)=-4x2+x+1 by using the vertex formula to determine the vertex of the graph of the function.

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please help me {x-2}<1 need to graph it (Find all real roots of the following equations:
4) (2x - 3)2 = (3x + 1)2;
(5) 3t 4 - 8t 2 + 5 = 0;
(6) 3x3 - 5x2 - 3x + 5 = 0.
marks) Factorize the following expressions:
(1)