Mathematics: Which of the following equations has a graph in the xy-plane for which y is always greater than or equal to -1 ? A) y = |x| - 2 B) y = x2 - 2 C) y = (x - 2)2 D) y = x3 - 2

Which of the following equations has a graph in the

manueelaa

28.07.2021

$n = - 4 \: or \: n = 8$

Step-by-step explanation:

If the point (2,n) lies on the circle whose equation is:

$( {x - 4)}^{2} + {(y - 2)}^{2} = 40$

Then this point must satisfy the equation of the circle:

We substitute x=2 and y=n into the equation to get:

$( {2 - 4)}^{2} + {(n - 2)}^{2} = 40$

We simplify:

$4+ {(n - 2)}^{2} = 40$

This implies that,

${(n - 2)}^{2} = 40 - 4$

${(n - 2)}^{2} =36$

Take square root;

$n - 2 = \pm \sqrt{36}$

Evaluate:

$n - 2 = \pm6$

$n =2 \pm6$

$n =2 - 6 \: or \: n = 2 + 6$

$n = - 4 \: or \: n = 8$

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