SOLUTION: Could anyone please offer their help on this one? I studied the text and can't figure this out. Thank You. Compare the graph of the given quadratic function f with the graph of

Algebra ->  Graphs -> SOLUTION: Could anyone please offer their help on this one? I studied the text and can't figure this out. Thank You. Compare the graph of the given quadratic function f with the graph of       Log On


   

Question 134222: Could anyone please offer their help on this one? I studied the text and can't figure this out. Thank You.
Compare the graph of the given quadratic function f with the graph of y=x^2.
f(x)=(x-2)^2+3
Thanks again!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's graph the first equation y=x%5E2

graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%29+


Now let's add the graph of y=%28x-2%29%5E2%2B3

graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2C%28x-2%29%5E2%2B3%29+ Graph of y=x%5E2 (red) and y=%28x-2%29%5E2%2B3 (green)


Notice how the green graph, which is the equation y=%28x-2%29%5E2%2B3, is simply the same as the original graph, but has been shifted 2 units to the right and 3 units up.


Note: The 2 unit shift to the right corresponds to the 2 in %28x-highlight%282%29%29%5E2%2B3 and the 3 unit shift up corresponds to the 3 in %28x-2%29%5E2%2Bhighlight%283%29