Question

When graphed, which parabola opens downward? y = –3x2     y = (x – 3)2    y = x2 – 3

Answer 1

The answer to this question is y = –3x^2, just had this on e2020 :)

Answer 2

we know that

the equation of a vertical parabola into vertex form is equal to

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

where

(h,k)-------> is the vertex of the parabola

if
`a > 0` -------> the parabola open upwards

if
`a < 0` -------> the parabola open downwards

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

`a =-3`

so

`a < 0` -------> the parabola open downwards

the vertex is the point
`(0,0)` ------> is a maximum

therefore

`y=-3x^(2)` open downwards

case B)
`y=(x-3)^(2)`

`a =1`

so

`a > 0` -------> the parabola open upwards

the vertex is the point
`(3,0)` --------> is a minimum

therefore

`y=(x-3)^(2)` open upwards

case C)
`y=x^(2)-3`

`a =1`

so

`a > 0` -------> the parabola open upwards

the vertex is the point
`(0,-3)` --------> is a minimum

therefore

`y=x^(2)-3` open upwards

therefore

the answer is

`y=-3x^(2)` open downwards