For each of the the following quaratic equations,
find
(a)the optimum value,
(b)(i)the direction of opening
(ii)the vertex,
(iii)the axis of symmetry
of its graph by completing square
1. y=2(2x-x)(x+2)-4x
2.y=(x+1)^2+(2(x-1)
1)y=2(x)(x+2)-4x
y=2x^2
a)(0,0)
b)i)upward
ii)(0,0)
iii)x=0
2)y=(x^2+2x+1)+2x-2
y=x^2+4x-1
y=(x+2)^2-5
a)(-2,-5)
b)i)upward
ii)(-2,-5)
iii)x=-2
3.In the figure,the base and the height of a parallelogram are (6-x)cm and 2x cm respectively.
(a)Find the maximum area of this parallelogram.
(b)Find the height and the base of the parallelogram when the area is maximum.
3a)let A=area parallelogram
A=(6-x)(2x)=12x-2x^2=-2(x^2-6x)=-2(x-3)^2+18
the maximun area of it is 18cm^2
b)the height=2(3)=6cm
the base=(6-3))=3cm
