SOLUTION: 9. Write an equation that defines the graph of y = x2 after it is shifted vertically 2 units up and horizontally 3 units left.

Algebra ->  Linear-equations -> SOLUTION: 9. Write an equation that defines the graph of y = x2 after it is shifted vertically 2 units up and horizontally 3 units left.       Log On


   

Question 1048834: 9. Write an equation that defines the graph of y = x2 after it is shifted vertically 2 units up and horizontally 3 units left.
Found 2 solutions by MathLover1, josmiceli:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

y=x%5E2%2Bk is a vertical+shift, up if k%3E0 and down if k%3C0
+y=%28x-h%29%5E2 is a horizontal shift, left if h%3C0 and right if+h%3E0

an equation that defines the graph of y+=+x%5E2 after it is shifted vertically 2+ units up is: y+=+x%5E2%2B2
and after it is shifted horizontally 3 units left.:
y+=+%28x-%28-3%29%29%5E2%2B2
y+=+%28x%2B3%29%5E2%2B2

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2C+%28x%2B3%29%5E2%2B2%29+


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+y+=+x%5E2+
Just shifting 2 units up, I get:
+y+-+2+=+x%5E2+
Note that the point that was formerly
( 0,0 ) is now ( 2,0 )
------------------------
Shifting 3 units to the left, I get:
+y+-+2+=+%28+x+%2B+3+%29%5E2+
Note the point that was formerly
(0,0) is now ( 2, -3 )
------------------------------
Here's the plot of 1st equation and
the final equation:
+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2C+%28+x%2B3+%29%5E2+%2B+2+%29+