Question

Which system of inequalities is graphed below?

Answer 1

A. y < x² + 6 ; y > x² - 4

Explanation:

The area between the two functions represent the system of inequalities graphed.

Given the parent function f(x) = x², if we translated 6 units up we get g(x) = x² + 6, which corresponds to the upper function in the graph. Then, one restriction is y < x² + 6 (notice that the dotted line indicates the equal sign is not included).

If we translate f(x) 4 units down, we get h(x) = x² - 4, which corresponds to the lower function in the graph. Then, the other restriction is y > x² - 4 (again, the equal sign is not included).

Taking for example the point (0, 0), which correspond to the solution of the system, we get

0 < 0² + 6

0 < 6

0 > 0² - 4

0 > -4

which is correct

Answer 2

Option A

`y>x^(2) -4`

`y<x^(2) +6`

Explanation:

we know that

1) The equation of the vertical parabola with y-intercept -4 is equal to

`y=x^(2) -4`

The solution of the inequality is the shaded area above the dashed line

so

The inequality must be

`y>x^(2) -4`

2) The equation of the vertical parabola with y-intercept 6 is equal to

`y=x^(2)+6`

The solution of the inequality is the shaded area below the dashed line

so

The inequality must be

`y<x^(2) +6`

therefore

The system of inequalities graphed is

`y>x^(2) -4`

`y<x^(2) +6`