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(Follow on from previous question) A curve has equation y= x^2+3x+2. Use your previous results to i) find the vertex of the curve ii) find the equation of the line of symmetry of the curve

i) y = x 2 +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 (minimum point) is (-3/2,-1/...
RI
Answered by Ross I. • Maths tutor
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Express x^2+3x+2 in the form (x+p)^2+q, where p and q are rational numbers.

x 2 +3x+2 = (x+p) 2 +q (x+3/2) 2 = x 2 +3x+9/4 x 2 +3x+2 = (x+3/2) 2 -9/4+2 x 2 +3x+2 = (x+3/2) 2 -1/4
RI
Answered by Ross I. • Maths tutor
8552 Views

Discuss the impact of an urban transport sustainability scheme you have studied.

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 34,000 ...
OT
Answered by Oscar T. • Geography tutor
2484 Views

Solve 8^x + 4 = 4^x + 2^(x+2).

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 problem (at least at th...
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Answered by Sachin A. • MAT tutor
1793 Views

Perfect competition theory is based on very unrealistic assumptions. Evaluate whether such a theory is useful in explaining the behaviour of real world firms.

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), identical ...
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Answered by Konrad V. • Economics tutor
20358 Views