For each of the following quadratics, determine if the equation has a max or a min, determine the value of the max or min, the direction of opening and the vertex.
y = -2(x + 3)2 – 4
y = 4(x – 3)2 + 7
y = -x2
y = -½(x + 6)2
Rewrite the quadratics in the standard form
y(x)=a(x-h)+k
when
a<0, there is a maximum (concave downwards)
a>0, there is a minimum (concave upwards)
The maximum or minimum occurs when x=h
The vertex is the value of the max/min.
and occurs at x=h, i.e.
(h,k)
For example,
y(x) = -2(x + 3)² – 4
a=-2, therefore there is a maximum at x=-3, and the vertex is at (-3,-4).