Respuesta :

calculista

Answer:

Option A

[tex]y>x^{2} -4[/tex]

[tex]y<x^{2} +6[/tex]

Step-by-step explanation:

we know that

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

[tex]y=x^{2} -4[/tex]

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

so

The inequality must be

[tex]y>x^{2} -4[/tex]

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

[tex]y=x^{2}+6[/tex]

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

so

The inequality must be

[tex]y<x^{2} +6[/tex]

therefore

The system of inequalities graphed is

[tex]y>x^{2} -4[/tex]

[tex]y<x^{2} +6[/tex]

Answer:

A. y < x² + 6 ; y > x² - 4

Step-by-step 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

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