Question

Which function has vertex (-3, -1) and contains the point (1, -9)​

Answer 1

`y=-(1/2)(x+3)^(2) -1`

Explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

`y=a(x-h)^(2) +k`

where

(h,k) is the vertex of the parabola

In this problem the vertex is the point
`(-3,-1)`

substitute

`y=a(x+3)^(2) -1`

Observing the problem we have two cases that have the same vertex

case A)
`y=-(1/2)(x+3)^(2) -1`

case B)
`y=-(5/8)(x+3)^(2) -1`

Verify each case with the point
`(1,-9)`

substitute the value of x and the value of y in the equation and then compare the result

case A)
`-9=-(1/2)(1+3)^(2) -1`

`-9=-9` -----> is true

case B)
`-9=-(5/8)(1+3)^(2) -1`

`-9=-11` ------> is not true

therefore

the function is
`y=-(1/2)(x+3)^(2) -1`