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

Correct choices are and

Step-by-step explanation:

Consider all options.

1. Simplify the equation of parabola

Vertex coordinates are (1,3), p=4, then focus coordinates are (1,1) (parabola branches go down in y-direction). This option is false, because vertex and focus lie in Ist quadrant.

2. Simplify the equation of parabola

Vertex coordinates are (3,-2), p=8, then focus coordinates are (-1,-2) (parabola branches go left in x-direction). This option is true, because vertex lies in IVth quadrant and focus lies in 3rd quadrant.

3. Simplify the equation of parabola

Vertex coordinates are (9,-5), p=18, then focus coordinates are (0,-5) (parabola branches go left in x-direction). This option is false, because vertex lies in IVth quadrant and focus lies on the y-axis.

4. Simplify the equation of parabola

Vertex coordinates are (-4,-7), p=16, then focus coordinates are (-4,1) (parabola branches go up in y-direction). This option is true, because vertex lies in 3rd quadrant and focus lies in 2nd quadrant.

5. Simplify the equation of parabola

Vertex coordinates are (-5,-2), p=8, then focus coordinates are (-1,-2) (parabola branches go right in x-direction). This option is false, because vertex and focus lie in 3rd quadrant.

6. Simplify the equation of parabola

Vertex coordinates are (-5,5), p=12, then focus coordinates are (-5,-1) (parabola branches go down in y-direction). This option is true, because vertex lies in 2nd quadrant and focus lies in 3rd quadrant.

v = 1/3 a^2h

step-by-step explanation:

the volume is 1/3 a^2h.

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.