Question

Write a function for the graph described as a transformation of y=x^2.

12. y=x^2 experiences a vertical stretch of factor 2 and then a shift right of 3 units.

Answer 1

\[y=a(x-h)^2+k\]
a = vertical stretch factor
h = horizontal shift
k = vertical shift

Answer 2

you don't have a vertical shift, so ignore the k = 0. Plug in the numbers for a and h.

Answer 3

\[y=2(x-3)^{2}\]

Answer 4

is that right?

Answer 5

yes

Answer 6

thank you!

Answer 7

you're welcome

Answer 8

can you check another question i have? @peachpi

Answer 9

ok

Answer 10

y=x^2 experience a shift left by 2 units, then a horizontal shrink of factor 1/2 then a shift down 5 units
my answer : y=(x-1/2)^2

Answer 11

horizontal shrinks/stretches are multiplied by the x from the inside.
\[y=a(bx-h)^2+k\]
Use that as your basic formula. a, h, and k are explained above. \(b\) is the horizontal shrink/stretch factor.

The "default" numbers for a and b are 1, and for h and k it's 0.

In your problem you have
shift left, so h = -2
horizontal shrink, so b = 1/2
vertical shift down, so k = -5.
They don't say anything about vertical stretch/shrink, so leave it as 1.

\[y=\left( \frac{ 1 }{ 2 }x+2 \right)^2-5\]

Answer 12

thanks for explaining

Answer 13

you're welcome.

Answer 14

fyi pictures are better than words :) http://www.regentsprep.org/regents/math/algtrig/atp9/funclesson1.htm