Select the correct equations in the image.

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

The equations of the parabolas whose focus and vertex lie in different quadrants are;

The third equation and the sixth equation

Step-by-step explanation:

We analyse each of the equations as follows

Vertex = V(h, k)

Focus = F(h, k+p)

First equation

a = -1/8

b = 1/4

c = 23/8

k = 3

h = 1 Hence same quadrant

Second equation

a = 1/32

b = 1/4

c = -13/2

h = -4

k = -7 same quadrant

Third equation

a = -1/16

b = -1/4

c = 11/4

k = 3

h = -2 Hence different quadrants

Fourth equation

a = 1/16

b = 1/4

c = -19/4

h = -2

k = -5 The same quadrant

Fifth equation

a = -1/36

b = -5/18

c = 299/36

k = 620.56

h = 149.5 The same quadrant and

Sixth equation

a = -1/24

b = -5/12

c = 95/24

h = -5

k ≈ 5   Hence different quadrants

Hence the equations of the parabolas whose focus and vertex lie in different quadrants are the third and sixth equations presented as follows;

Third equation:

Sixth equation:

.

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction

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