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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.

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• 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¿
• 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?
• 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.
• How can you solve the problem if you don't have the graph to help you?
• Start from a parent quadratic function y = x^2. Adding parameters to this function shows both scaling, reflecting, and translating this function from the original without graphing. So you may see a form such as y=a(bx-c)^2 + d. The parabola is translated (c,d) units, b reflects across y, but this just reflects it across the axis of symmetry, so it would look the same. A negative a reflects it, and if 0<a<1, it vertically compresses the parabola, and if x>1, it vertically stretches the parabola. We can do a lot with equations.
• How would reflecting across the y axis differ? I'm so confused.
(1 vote)
• this really doesnt help at all, im still just as confused, just about different things now