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,
+130081 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
