SOLUTION: sketch the graph of {{{y=2+3(x+1)^2}}}, not by plotting points but by starting with {{{g=x^2}}} and using translations. Describe the steps you take in getting the graph of y.

Algebra ->  Algebra  -> Graphs -> SOLUTION: sketch the graph of {{{y=2+3(x+1)^2}}}, not by plotting points but by starting with {{{g=x^2}}} and using translations. Describe the steps you take in getting the graph of y.       Log On

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Question 30502: sketch the graph of y=2%2B3%28x%2B1%29%5E2, not by plotting points but by starting with g=x%5E2 and using translations. Describe the steps you take in getting the graph of y. Thank you!
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
y=2%2B3%28x%2B1%29%5E2

Starting with y=x%5E2, first we move the curve by 1 unit to the left to give y=%28x%2B1%29%5E2, as seen by +graph%28300%2C300%2C-4%2C3%2C-4%2C10%2C%28x%2B1%29%5E2%29+

Next, we stretch it by a factor of 3, anchored still on the x-axis at (-1,0). Look at the graph here and note the y-intercept is now at y=3, instead of y=1: +graph%28300%2C300%2C-4%2C3%2C-4%2C10%2C3%28x%2B1%29%5E2%29+

Finally, we will move the whole curve up by 2 units, so that the vertex is now at (-1,2) and the y-intercept is at y=5: +graph%28300%2C300%2C-4%2C3%2C-4%2C10%2C2%2B3%28x%2B1%29%5E2%29+

jon.