Question

Match the equations representing parabolas with their directrixes. y + 8 = 3(x + 2)2 y − 14 = -(x − 3)2 y + 7.5 = 2(x + 2.5)2 y − 17 = -(x − 3)2 y + 7 = (x − 4)2 y − 6 = -(x − 1)2 Directrix Equation of Parabola y = -7.25 arrowRight y = 6.25 arrowRight y = 17.25 arrowRight y = 14.25 arrowRight

Answer 1

Part 1)
`y+8=3(x+2)^(2)` ----->
`y=-8.08`

Part 2)
`y-14=-(x-3)^(2)` ---->
`y=14.25`

Part 3)
`y+7.5=2(x+2.5)^(2)` ---->
`y=-7.625`

Part 4)
`y-17=-(x-3)^(2)` ----->
`y=17.25`

Part 5)
`y+7=(x-4)^(2)` ---->
`y=-7.25`

Part 6)
`y-6=-(x-1)^(2)` ---->
`y=6.25`

Explanation:

we know that

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

`y-k=(1)/(4p)(x-h)^(2)`

where

(h,k) is the vertex

The directrix is

`y=k-p`

case 1) we have

`y+8=3(x+2)^(2)`

the vertex is the point (-2,-8)

`(1)/(4p)=3`

`p=(1)/(12)`

The directrix is equal to

`y=-8-(1)/(12)=-8.08`

case 2) we have

`y-14=-(x-3)^(2)`

the vertex is the point (3,14)

`(1)/(4p)=-1`

`p=-(1)/(4)`

The directrix is equal to

`y=14+(1)/(4)=14.25`

case 3) we have

`y+7.5=2(x+2.5)^(2)`

the vertex is the point (-2.5,-7.5)

`(1)/(4p)=2`

`p=(1)/(8)`

The directrix is equal to

`y=-7.5-(1)/(8)=-7.625`

case 4) we have

`y-17=-(x-3)^(2)`

the vertex is the point (3,17)

`(1)/(4p)=-1`

`p=-(1)/(4)`

The directrix is equal to

`y=17+(1)/(4)=17.25`

case 5) we have

`y+7=(x-4)^(2)`

the vertex is the point (4,-7)

`(1)/(4p)=1`

`p=(1)/(4)`

The directrix is equal to

`y=-7-(1)/(4)=-7.25`

case 6) we have

`y-6=-(x-1)^(2)`

the vertex is the point (1,6)

`(1)/(4p)=-1`

`p=-(1)/(4)`

The directrix is equal to

`y=6+(1)/(4)=6.25`