Given the function h(x)=x^2+14x+41, to solve by completing square we procced as follows;
x^2+14x+41=0
x^2+14x=-41
but;
c=(b/2)^2
and b=14
hence;
c=(14/2)^2=49
substituting the value of c in the expression we get:
x^2+14x+49=-41+49
x^2+14x+49=8
(x+7)^2=8
this can be written in vertex form;
h(x)=a(x-h)^2+k
where:
(h,k) is the vertex;
thus
(x+7)^2=8
h(x)=(x+7)^2-8
hence the vertex will be at the point:
(-7,-8)
You need 3 trucks of sand that hold 5 tons and 2 trucks that hold 3 tons to move all the sand in one trip
Translation:
R ( - 5, - 5 ) → R` ( - 4, 2 )
- 4 = - 5 + 1, 2 = - 5 + 7;
The translation rule:
( x , y ) → ( x + 1, y + 7 )
Coordinates of the point U are (- 5, 1 )
- 5 + 1 = - 4, 1 + 7 = 8
The image of U is :
U` ( - 4, 8 )
