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i) y = x²+3x+2 = (x+3/2)²-1/4Solution for (x+3/2) = 0 is x coordinate, which is x = -3/2Solution for y value is the additional constant, which is y = -1/4Therefore the vertex (minimu...

 x²+3x+2 = (x+p)²+q (x+3/2)² = x²+3x+9/4 x²+3x+2 = (x+3/2)²-9/4+2 x²+3x+2 = (x+3/2)²-1/4

Brighton, a sea-side city in the South-East of the United Kingdom, has a population of over 275,000 people which is expected to grow to 300,000 by 2030. This is in addition to a student population of 34,0...

Firstly, we want to notice that this question only involves powers of 2^x, ie.
(2^x)^3 + 4 = (2^x)^2 + 4(2^x)
so we can use the substitution u = 2^x to give
u^3 - u^2 - 4u + 4 = 0
The...

The main assumptions of the model of perfect competition are: the number of selling firms tends to infinite, both sellers and buyers are price takers (i.e. they cannot influence the market price), identic...