How is the graph of the parent function y=x2 transformed to produce the graph of y=3(x+1)??
It is translated 1 unit right and compressed vertically by a factor of 3.
It is translated 1 unit left and compressed vertically by a factor of 3.
It is translated 1 unit right and stretched vertically by a factor of 3.
It is translated 1 unit left and stretched vertically by a factor of 3.

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Ответ:

anthony1366

02.11.2022

Mathematics

$c) (x-h)^{2}+(y-v)^{2}=r^{2}$

Step-by-step explanation:

Hi There,

1. The Circle formula in its standard form is given by:

$(x-a)^{2}+(y-b)^{2}=r^{2}\Rightarrow C=(a,b)$

2) This coordinates a, b are the Center coordinates of the Center, a point distant from the circumference by the radius.

3) Because we can find derive this formula from that. (Check the graph below)

There's a point P(x,y) whose distance to C(h,v) is the radius, we need to calculate it numerically:

$r=\sqrt{(x-h)^{2}+(y-v)^{2}} \:or\:r^{2}=(x-h)^{2}+(y-v)^{2}\\r=\sqrt{x^{2}-2hx+h^{2}+y^{2}+2vy+v^{2}}\\r=\sqrt{x^{2}+h^{2}+y^{2}+v^{2}}\\(r)^{2}=(\sqrt{x^{2}+h^{2}+y^{2}+v^{2}})^{2}\\r^{2}=x^{2}+h^{2}+y^{2}+v^{2}\\r^{2}=x^{2}+y^{2}+h^{2}+v^{2}\\\\$

4) Hence, as the Center has its coordinates C(h,v) then its circle formula is:

$c) (x-h)^{2}+(y-v)^{2}=r^{2}$

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