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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

User Parth Vyas
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1 Answer

3 votes

Answer:

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

User Omarojo
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