# Precalculus 11

I just want to double check that I have this right. Write the new equation of the parabola
y=(x-3)^2-7 that is translated 4 units left, 5 units up & is compressed by a factor of 1/4

y=1/4(x+1)^2-2

Thanks a bunch :) ♡

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1. looks good

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2. y = f ( x + h )

translated left h units

In this case:

f ( x + 4 ) = ( x - 3 + 4 )² - 7 = ( x + 1 )² - 7

y = f ( x ) + k

translated up k units

In this case:

f ( x + 4 ) + k = f ( x + 4 ) - 7 + 5 = ( x + 1 )² - 7 + 5 = ( x + 1 )² - 2

y = ( 1 / m )· f ( x )

compressed vertically by a factor of 1 / m

In this case:

( 1 / 4 )·( x + 1 )² - 2

f ( n· x ) compressed horizonally by a factor of 1 / n

In this case:

f ( 4· x ) = ( 4 x + 1 )² - 2

If your functions is translated 4 units left, 5 units up and compressed vertically by a factor of 1 / 4 then:

( 1 / 4 )·( x + 1 )² - 2

If your functions is translated 4 units left, 5 units up and compressed horizonally by a factor of 1 / 4 then:

( 4 x + 1 )² - 2

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3. Thanks guys!:)

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