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Quadratic and Line Intersection
The quadratic y = x2 – 2 x – 1 and the line y = –8 x – 9 have points in common
at coordinates ( , )and ( , )

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Worked Solution:

Where the quadratic meets the line we have y = x2 – 2 x – 1 = –8 x – 9
=>x2 – 2 x – 1 = –8 x – 9
=>x2 + 6 x + 8 = 0
The quadratic factorizes: x2 + 6 x + 8 = (x + 4)(x + 2)
=> the quadratic is 0 when x = –4 and when x = –2
x = –4=>y = 23 and
x = –2=>y = 7
The two points common to the quadratic and the line are ( –4, 23) and ( –2, 7)

© MEI Produced by Dr Ron Knott, 20 July 2004, revised 12 May 2008
tom . button [AT] mei . org . uk 		Test reference: SimQuadLine.html?ref=1511