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#1 2006-09-10 06:30:05
- RickyOswaldIOW
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- Registered: 2005-11-18
- Posts: 212
Where does the curve meet the axis?
sketch the curve y= 9 - (x - 2)², showing the coordinates of the points at which the graph meets to coordinate axes.
I have produced this sketch, the maximum point (2,9) and it crosses the y axis at (0,5). I know to find the intersection of the x axis I must put y=0 i.e. y = 9 - (x - 2)² = 0. I can't remember how to solve this and it's been puzzling me all last night and today 
Firstly I multiply out the brackets to give
-(x - 2)² - 9
-x² + 4x + 4 - 9
-x² + 4x - 5
So,
-x² + 4x - 5 = 0
-x² + 4x = 5
Where do I go from here?
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#2 2006-09-10 06:59:15
- luca-deltodesco
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- Registered: 2006-05-05
- Posts: 1,470
Re: Where does the curve meet the axis?
theres no need to expand the equation, because you already have it in completed square form, which is an easy way to solve it
0 = 9 - (x-2)^2,
(x-2)^2 = 9
x-2 = ±3
x = 2±3 = -1, 5
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#3 2006-09-10 07:11:23
- krassi_holmz
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- Registered: 2005-12-02
- Posts: 1,905
Re: Where does the curve meet the axis?
Absolutely right.
Graphically:
Last edited by krassi_holmz (2006-09-10 07:12:40)
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#4 2006-09-10 07:38:20
- RickyOswaldIOW
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- Registered: 2005-11-18
- Posts: 212
Re: Where does the curve meet the axis?
Brilliant, thank you 
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