Which function is the result of translating f(x) = x^2 + 14 to the right 5 units and down 6 units? A) y = (x - 5)^2 + 6
B) y = (x - 5)^2 - 6
C) y= (x - 5)^2 + 8
D) y= (x - 5)^2 + 20

C.

Step-by-step explanation:

Transformations within the quadratic is given by the form:

Where a is the vertical stretch, h is the horizontal translations, and k is the vertical translations.

We have:

If we translate this 5 units to the right, we are letting h=5. This yields:

If we shift the function down 6 units, we are subtracting 6 from the function. This will yield:

Subtract:

Therefore, our answer is C.

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}