F.4 mathz,,about Quadratic Functions in Vertex Form

1. y=-x^2-3
when x = 0 , y obtains its maximum value -3
a)The vertex is (0,-3)
b)The axis of symmetry is x = 0
c)-3
2. y=-2(x-3)^2+5
when x = 3 , y obtains its maximum value 5
a)The vertex is (3,5)
b)The axis of symmetry is x = 3
c)5
3. y=-1/3(x+2)^2-3
when x = -2 , y obtains its maximum value -3
a)The vertex is (-2,-3)
b)The axis of symmetry is x = -2
c)-3
4. y=1/2(x+2/5)^2
when x = -2/5 , y obtains its minimum value 0
a)The vertex is (-2/5,0)
b)The axis of symmetry is x = -2/5
c)0
5. y=(x-a)^2-b
when x = a , y obtains its minimum value -b
a)The vertex is (a,-b)
b)The axis of symmetry is x = a
c)-b
6. y=-(x+2a)^2+b
when x = -2a , y obtains its maximum value b
a)The vertex is (-2a,b)
b)The axis of symmetry is x = -2a
c)b
So, from the above example:
y=a(x+h)^2+k
(-h,k) is the coordinates of the vertex
The axis of symmetry is x = -h
The optimum value is k (when a>0 , y has minimum value , a<0 , y has maximum value)