Question

The graph of y = x2 is shown below. Using complete sentences, explain how the graph of
y = –3(x – 2)2 + 1 would differ from this parabola.

Answer 1

When you add 1 to the function...you shift the parabola up 1 unit...

when you subtract 2 from the 'x'...you shift the parabola to the right 2 units

What happens when you multiply a number to the 'x'...?

Answer 2

im not sure

Answer 3

go down?

Answer 4

Here's a really good website to explain all the transformations

http://www.regentsprep.org/Regents/math/algtrig/ATP9/funclesson1.htm

Answer 5

ok i got nothing lol

Answer 6

@johnweldon1993

Answer 7

so it shifts up with +1 and
shifts to the right 2 when you subtract 2

Answer 8

the parabola will move on the x axis when you multiply?

Answer 9

@johnweldon1993

Answer 10

Oh sorry about that...

yes when you add the 1....you move the parabola up 1 on the y-axis
yes when you subtract 2 from the 'x' you move the parabola 2 units to the right on the x-axis

When you multiply a function by a number....*1) its a negative number so it flips the parabola upside down

2) when it is being multiplied by that..it is stretched vertically by a factor of that number...in this case...3

Answer 11

oh ok i understand. would that be my answer?

Answer 12

x ^{2}=y,it is an upward parabola with vertex (0,0)

\[y=-3\left( x-2\right)^{2} +1,\left( x-2\right)^{2}=- \frac{ 1 }{3}\left( y-1 \right)\]
it is a downward parabola with vertex (2,1)