Answer:
The correct option is C) <u>function (x-5)(x+1) has vertex (2,-9)</u>.
Step-by-step explanation:
The vertex of an up down facing parabola of the form y=ax²+bx+c is
option A) -(x-3)²
Rewrite in the form
Expand
The parabola parameters are: a = - 1, b = 6, c = - 9
simplify, 3
Plugin to find the value
If a<0, then the vertex is a maximum value.
If a>0, then the vertex is a minimum value.
since, a = - 1
Maximum (3,0)
option B) (x+8)²
Rewrite in the form
Expand
The parabola parameters are: a = 1, b = 16, c = 64
simplify, - 8
Plugin to find the value
If a<0, then the vertex is a maximum value.
If a>0, then the vertex is a minimum value.
since, a = 1
Minimum (-8,0)
option C) (x-5)(x+1)
Rewrite in the form
Expand
The parabola parameters are: a = 1, b = -4, c = -5
simplify, 2
Plugin to find the value
If a<0, then the vertex is a maximum value.
If a>0, then the vertex is a minimum value.
since, a = 1
Minimum (2,-9)
Hence, the correct option is C) <u>function (x-5)(x+1) has vertex (2,-9)</u>.