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ABSOLUTE VALUE Qs

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1. The graph of y = a|x+b|+c passes through points A = (3, 5), B = (7,
11), and C = (13, 17).
Find the values of a,

Feb 11, 2018

#1
+101090
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A = (3,5)   B  = (7, 11)   C  = ( 13,17)

Because of the nature of the points.....this graph will turn downward

The slope  of the line between (3,5) and ( 7,11)  is 6/4  =  3/2

And the equation of this line is

y  = (3/2) (x - 3) + 5    ⇒  (3/2)x + 1/2

And this line forms the "left " branch of the absolute graph

For the equation  of the line forming the other half of the graph...it will have a slope that is the negative of the first line and it will pass through ( 13, 17)

So the equation of this line is just

y = (-3/2) ( x - 13) + 17    ⇒  (-3/2)x  +  73/2

The intersection of these two lines will form the "vertex" of the function....so we have....

(3/2)(x) + 1/2  =  (-3/2)x + 73/2

3x    =  72/2

3x  = 36     ⇒  x  =  12

And y  =  (3/2)(12) + 1/2  =  18.5

So   b =  12   and c =  18.5

To find "a"  we can use any of the points

So we have that

5  =  a l 3 - 12  l  + 18.5

-13.5  = a (9)

a  =  -13/5 / 9   =   -3/2  =  -1.5

Here's the graph of the lines and the absolute value graph itself :

https://www.desmos.com/calculator/1eyojys50i

Feb 11, 2018