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# Scaling & reflecting parabolas

The graph of y=k⋅x² is the graph of y=x² scaled by a factor of |k|. If k<0, it's also reflected (or "flipped") across the x-axis. In this worked example, we find the equation of a parabola from its graph.

## Want to join the conversation?

• Where/How did he get 1/4? Why isn't the work for THAT shown?
• It helps me to compare it to the function y = -x^2, so when x = 1 or -1, y = 1, you have points (1,-1)(-1,-1). So when you widen this parabola, you need some fraction in front. When x = 2, you get x^2 = 4, so what do you fraction do you need to have this give a y value of -1? You have to multiply by the negative reciprocal, and that is where the -1/4 comes from, f(x) = - 1/4 x^2, thus f(2) = -1/4 (2)^2 = -1. So if you moved it over one more to get to x = 3, the fraction would have to be -1/9, etc.
• Does y2/y1 gives the scale value? For example, in this video, y1 (when x = 1) = 1 and y2 = -1/4, so -1/4/1 gives -1/4.
• Yes you are absolutely correct. The scale value is essentially the ratio between the the y-value of the scaled parabola to the y-value of the original parabola at a given x-value.
• How can you solve the problem if you don't have the graph to help you?
• in what situation? What kind of problem would you have like this¿
• Hello. I've just finished the Algebra 1 course and was wondering: Should I do Algebra 2 now or Geometry? Thanks a lot to whoever answers this!
• In general, the pathway is Algebra 1, then Geometry, then Algebra 2.

This is for two reasons:

1) The topics in Geometry are generally easier than the ones in Algebra 2

2) Some Algebra 2 topics are much easier to understand after learning Geometry. For example, in Geometry, you are introduced to transformations by doing them with basic shapes. Then, in Algebra 2, you take it up a notch and do the same transformations but with graphs of functions.

So, I highly recommend Algebra 2 comes after. But it is definitely doable to learn it first… it is up to you!

Hope this helps!
• How do you find the stretch/shrink factor? As in, how did he get 1/4?
• For the parent function, y=x^2, the normal movement from the origin (0,0) is over 1 (both left and right) up one, over 2 (both left and right) up 4, over 3 (both ...) up 9 based on perfect squares. So your scale factor compares to that, in this case, over 2 goes down 1, so it is 1/4 that of the parent function. The same is true at 4 which is down 4 (which is 1/4 of the parent function which would be at 16 (4^2=16). So the scale factor is a change from the parent function.
• The parabola y=x^2

is scaled vertically by a factor of 7.
What is the equation of the new parabola?

what would be the answer for this?
• Shouldn't -f(x) the inverse of f(x) be y = -(x^2) instead of -x^2 because -2^2 = 2^2 (so if x = 2 | x = -2, y = 4 in both cases).
(1 vote)
• -x^2 and -(x^2) mean the same thing.
I think you are confusing -x^2 with (-x)^2
An exponent will only apply to the sign if the sign and number/variable are written inside parentheses.
-2^2 = -(2*2) = -4
(-2)^2 = (-2)(-2) = +4

Hope this helps.
• What if they give you coordinates
• I treat it the same way as pattern in sequence.
Original value of y is: 1
After transformation y is: -4
To get from 1 to -4, i can multiply it by -4.
So from x^2 we get -4x^2.

But if it's shifted to right or left... I don't know tbh