Question

Which points justify shading inside the conic inequality 8x² - 12x + 4y² + 4y – 20 ≤ 0 ?

Check all that apply.
a. (-1,-2)
b. (-1,-1)
c. (0,0)
d. (0,2)
e. (1,-2)

Answer 1

The given conic inequality has no shading inside, so none of the points justify shading.

Step-by-step explanation:

To determine which points justify shading inside the conic inequality 8x² - 12x + 4y² + 4y - 20 ≤ 0, we need to find the solution set of the inequality.

1. Rewrite the inequality in standard form:

4y² + 4y - 8x² + 12x - 20 ≤ 0

2. Use factoring or the quadratic formula to solve for y:

y = (-1 ± √(1 - 4(-8)(-20))) / (2(4))

y = (-1 ± √(1 - 640)) / 8

y = (-1 ± √(-639)) / 8

Since there is no real solution for y, the inequality has no shading inside.

Therefore, none of the given points, (-1,-2), (-1,-1), (0,0), (0,2), and (1,-2), justify shading inside the conic inequality.