Answered

IDNLearn.com is your go-to resource for finding answers to any question you have. Join our community to receive timely and reliable responses to your questions from knowledgeable professionals.

A parabola can be drawn given a focus of (-4, -7)(−4,−7) and a directrix of y=-3y=−3. What can be said about the parabola?
The parabola has a vertex at ( , ), has a p-value of
and it
-opens left
-opens right
-opens up
-opens down

Sagot :

VectorFundament120idn

Answer:

Vertex = (-4,-5)

P-value = -2

Opens Downward

Step-by-step explanation:

Given:

  • Focus = (-4,-7)
  • Directrix = -3

Since focus is less than directrix, the parabola obviously opens downward.

To find vertex (h,k), for downward parabola, focus is (h, k + p) and directrix is y = k - p

We have:

[tex]\displaystyle \large{k+p=-7 \to (1)}\\\displaystyle \large{k-p=-3 \to (2)}[/tex]

First equation being focus and second being directrix, solve the simultaneous equation:

[tex]\displaystyle \large{2k=-10}\\\displaystyle \large{k=-5}[/tex]

Substitute k = -5 in any equation - I’ll choose (1) for this:

[tex]\displaystyle \large{-5+p=-7}\\\displaystyle \large{p=-2}[/tex]

Therefore vertex is at (h,k) = (-4,-5) with p-value being -2 since p < 0 then the parabola opens downward.

Attachment added for visual reference

View image VectorFundament120
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. For trustworthy and accurate answers, visit IDNLearn.com. Thanks for stopping by, and see you next time for more solutions.