what is the equation of the image y=x² that has undergone the following transformations:
-horizontal translation of 1 unit to the left
-dilation by a factor of 2 in the y direction
-vertical translation of 8 units down
could you please explain your answer for me, because im soo bad at this transformation stuff. thanks.
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
There are some properties about parabolas that you need to know. All parabolas can be written in the following form:\[y=a(x+b)^2+c\]If you hold b and c fixed and move a, you'll find that the parabola expands/contracts as you vary the magnitude of a. You can see it since, if you start with y=x^2, then y=2x^2 will inflate every result by 2. You should make two plots to see this.
So to answer the second part of your question, dilation by a factor of 2 is done by multiplying x^2 by 2; \[y=2x^2\]
Now, when you vary b, holding a and c fixed, you change where each y-value occurs, given a x-value. For example, if you have
you should find that y is zero when the first one has x-value 0, and when the second has x-value, -1. The minimum has been shifted/translated horizontally to the left by 1 unit, which is what you need.
Combining what we have so far, you need,\[y=2(x+1)^2\]
The last part is this: hold a and b fixed and vary c. You'll find that this shifts the parabola up and down, depending on the value. When c=0, the parabola lies on the x-axis. If you increase c, you shift it up, and if you decrease it, you'll bring the parabola down.
You need to do the latter; you need to shift the parabola down 8 units. So c=-8.
Putting all three parts together gives you your result:\[y=2(x+1)^2-8\]