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 :) ♡

looks good

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

Thanks guys!:)

You got it almost right! Let's go through the steps to double-check the equation of the parabola after the given transformations.

Original equation: y = (x - 3)^2 - 7

1. Translation 4 units left:
To move the parabola 4 units to the left, we need to add 4 to the x-coordinate inside the equation.

Transformed equation: y = (x + 4 - 3)^2 - 7
Simplifying: y = (x + 1)^2 - 7

2. Translation 5 units up:
To move the parabola 5 units up, we need to add 5 to the y-coordinate outside the equation.

Transformed equation: y = (x + 1)^2 - 7 + 5
Simplifying: y = (x + 1)^2 - 2

3. Compression by a factor of 1/4:
To compress the parabola, we need to multiply the x-coordinate by the reciprocal of the compression factor, which in this case is 1/4. We also need to adjust the y-coordinate if necessary.

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

So, the correct equation of the parabola after the given transformations is:
y = (1/4)(x + 1)^2 - 2

You were really close! Great job! If you have any more questions, feel free to ask.