Answer:
Maximum: (-1,9)
Step-by-step explanation:
Vertex form of the quadratic function
If the graph of the quadratic function has a vertex at the point (h,k), then the function can be written as:
[tex]y=a(x-h)^2+k[/tex]
Where a is the leading coefficient.
We are given the following function:
[tex]y =-2x^2-4x+7[/tex]
To find the vertex, we need to complete squares. First, factor -2 on the first two terms:
[tex]y =-2(x^2+2x)+7[/tex]
The expression in parentheses must be completed to represent the square of a binomial. Adding 1 and subtracting 1:
[tex]y =-2(x^2+2x+1- 1)+7[/tex]
Taking out the -1:
[tex]y =-2(x^2+2x+1)+2+7[/tex]
Factoring the trinomial and operating:
[tex]y =-2(x+1)^2+9[/tex]
Comparing with the vertex form we have
Vertex (-1,9)
Leading coefficient: -2
Since the leading coefficient is negative, the function has a maximum value at its vertex, i.e.
Maximum: (-1,9)
