Transformations of y = x^2

[noobzilla]

Can someone help me get this clear?

For the function y = (3x + 7)^2

A suitable description of the transformation would be that y = x^2 has been horizontally translated 2.333 units to the left and it has also been horizontally compressed by a factor of 1/3.

is this correct?

[stapel_eliz]

If your "base" function is y = x², then your new function is y = (3(x + 7/3))². Using the exact values (almost uniformly the safer choice), the vertex has been shifted 7/3 to the left, and the parabola is only 1/3 as wide (or, to look at it another way, it is growing three times as fast).

So my only suggestion would be to edit your solution to use the exact value. Good job!

[noobzilla]

Thank you so much!!! you always help me figure these things out and I'm grateful for that.

Though I'm going to mention that I asked my teacher about this and he said to work it out by expanding it which would leave me with ax^2 + bx + c, but it still isn't a convinient way to look at it because I would have to complete the square having 9x^2 + 42x + 49, which will then factor to an equation with fractions. I think your approach is most suitable and uses exacts values, even if my teacher wants it the other way.

Thanks again!