Answer:
[tex]y=-(1/2)(x+3)^{2} -1[/tex]
Step-by-step explanation:
we know that
The equation of a vertical parabola in vertex form is equal to
[tex]y=a(x-h)^{2} +k[/tex]
where
(h,k) is the vertex of the parabola
In this problem the vertex is the point [tex](-3,-1)[/tex]
substitute
[tex]y=a(x+3)^{2} -1[/tex]
Observing the problem we have two cases that have the same vertex
case A) [tex]y=-(1/2)(x+3)^{2} -1[/tex]
case B) [tex]y=-(5/8)(x+3)^{2} -1[/tex]
Verify each case with the point [tex](1,-9)[/tex]
substitute the value of x and the value of y in the equation and then compare the result
case A) [tex]-9=-(1/2)(1+3)^{2} -1[/tex]
[tex]-9=-9[/tex] -----> is true
case B) [tex]-9=-(5/8)(1+3)^{2} -1[/tex]
[tex]-9=-11[/tex] ------> is not true
therefore
the function is [tex]y=-(1/2)(x+3)^{2} -1[/tex]
