Answer:
C
Step-by-step explanation:
We can use the vertex form of a quadratic equation, given by:
[tex]f(x)=a(x-h)^2+k[/tex]
Where a is the leading coefficient and (h, k) is the vertex.
We are given that the vertex is (-3, 1).
Hence, h = -3 and k = 1. By substitution:
[tex]f(x)=a(x-(-3))^2+(1)[/tex]
Simplify:
[tex]f(x)=a(x+3)^2+1[/tex]
With this, we can eliminate B and D.
Notice that our parabola is curving downwards.
Therefore, our leading coefficient must be negative.
The only choice that leaves us with is C.
So, our function is:
[tex]f(x)=-(x+3)^2+1[/tex]
And our final answer is C.
