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A curve has the equation y = 4x^2 + 5x + 3 and a line has the equation y = x + 2. Show that the line and the curve have one point of intersection.

Set the equations equal to each other: 4x^2 + 5x + 3 = x + 2Collect terms and set equal to 0: 4x^2 + 4x + 1 = 0Factorise the equation: (2x + 1)(2x + 1) = 0Can now find the value of x: 2x + 1 = 0, therefore 2...
FG
Answered by Francesca G. • Maths tutor
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A curve has the equation y=x^2+4x+4 and a line has the equation y=2x+3. Show the line and curve have only one point of intersection and find its coordinate..

First set the equations equal to each other: x^2+4x+4 = 2x+3.Rearrange for x in form ax^2+bx+c : x^2+2x+1=0Factorise: (x+1)^2=0. Repeated root, hence only one intersection. x=-1. Using y=2x+3, y=1. So coordi...
EF
Answered by Ewan F. • Maths tutor
5178 Views

Discuss the depiction of nature in two paintings by British artists.

The way in which British artists depicted nature changed considerably as different artists of different periods adapted it to their contemporary. Before the eighteenth-century paintings of nature was seen as...
JS
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Name and describe the type of bonding in H2O

The bonds in H 2 O are covalent bonds. Covalent bonds are formed when two atoms share a pair of electrons, often where one electron is donated by each atom. This forms a bond as there is an electrostatic att...
WS
Answered by William S. • Chemistry tutor
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(Note this is the kind of exercise I would ask someone who is doing further maths and especially someone MAT/STEP) Sketch the graph of y=sin(1/x)

First of all we want to think about the general behaviour of the function. Does it grow as x grows? Does it oscillate? Does it tend to a limit? We also need to think about if there are any worrying points in...
JT
Answered by James T. • MAT tutor
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