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.

step-by-step explanation:

no, her answer is not correct.   we square the lengths of all sides and then determine whether the pythagorean theorem holds here:

9² + 15² = 306.   this is not equal to the square of the longest side ( that square being 395.   answer c is correct.