Question

Which statement describes the translation of the graph of y = −2(x − 3)2 + 5 from standard position?

a)Moved up and to the right
b)Moved up and to the left
c)Moved down and to the right
d)Moved down and to the left

Answer 1

@Noland__DeWitte see if you can figure this one out :)?

Answer 2

brb k?

Answer 3

Alrighty

Answer 4

If the standard graph is
\(f(x)=x^2\), then the modified graph is
\(g(x)=a(x-h)^2+k\)
where
a=vertical scaling factor,
stretches when a>1
compresses when 0<a<1
stretches and reflects about the x-axis when a<-1
compresses when -1<a<0
h=horizontal translation (positive to the right)
k=vertical translation (positive upwards)

Example:
Find translation of
\(y=3(x+5)^2-2\)
First rewrite it as
\(y=3(x-(-5))^2-2\)
which gives
a=3, h=-5, k=-2
so the graph of \(y=x^2\) has been stretched vertically by a factor of 3, translated to the left by 5 (h=-5) , and downwards by 2 (k=-2).
The results of the \(example\) are shown in the following attachment.

Answer 5

ahh ok..so would the answer to my original question be d?

Answer 6

@mathmate

Answer 7

Parenthesis lie when translating graphs, negatives become positives and positives become negatives. Which means, -3 would be +3 and +5 would stay the same. Therefore, the graph would move up and to the right.

Answer 8

I hope you're right haha thanks

Answer 9

I'm 99% sure

Answer 10

could you help me with another one like this?

Answer 11

@gypsy1234
If you would rewrite the expression in the form
\(y=a(x-h)^2+k\)
you will find that h=3, k=5, a=-2,
so that in addition to flipping upside-down, stretched vertically, the vertex is translated by (3,5), and everything will make sense.
I would put @FireWolfSpirit 's statement
"Therefore, the \(graph\) would move up and to the right."
more as "Therefore, the \(vertex\) would move up and to the right." since the graph is flipped.