Question

Based on the the equations of the parabolas, identify each parabola whose focus and vertex lie in different quadrants.

Answer 1

y=-(x^2/8)+(x/4)+(23/8)

x=-(y^2/36) - (5y/18) + (299/36)

y=(x^2/32) + (x/4) - (13/2)

x=(y^2/16) + (y/4) - (19/4)

y=-(x^2/24) - (5x/12) + (95/24)

Answer 2

x=-(y^2/16) - (y/4) +(11/4)

Answer 3

.

Answer 4

?

Answer 5

@jane11509 ?

Answer 6

Nope :/ sorry

Answer 7

for the first one, \(y=-\dfrac{x^2}{8}+\dfrac{x}{4}+\dfrac{23}{8}\). From this, we can find the vertex of it, x\(= \dfrac{-b}{2a}= \dfrac{-(1/4)}{2(-1/8)}=1\) and then replace to get y=3. Hence the vertex is (1,3). The shape of the parabola is up-side down with vertex (1,3). we need do some more steps to figure out whether the focus and directrix are in the same quadrant or not.

\(y=-\dfrac{1}{8}(x^2-2x-23)\\=-\dfrac{1}{8}(x^2-2x+1-1-23)\\=-\dfrac{1}{8}(x+2)^2+3\)