Question

Identify the vertex of y = –1(x – 4)2 + 9 and tell whether it's a minimum or maximum.

Answer 1

The vertex equals 4,9

Answer 2

Vertex = (4, 9)

The vertex is the maximum

Explanation:

The vertex form of a quadratic of the form
`y=ax^(2) +bx+c` is
`y = a(x - h)^(2) + k` where
`(h,k)` are the coordinates of the vertex.

Comparing the vertx form of the quadratic to our quadratic
`y=-1(x-4)^(2)+9`, we can infer that
`h=4` and
`k=9`, so its vertex is the point (4, 9).

Now, in a parabola of the form
`y = a(x - h)^(2) + k` if
`a<0` the parabola open downwards and the vertex is its maximum, and if
`a>0` the parabola open upwards and the vertex is its minimum.

We know from our parabola that
`a=-1`. Since
`-1<0`, the vertex of our parabola is its maximum.

We can conclude that the vertex of our parabola is (4, 9) and is its maximum.