SOLUTION: Find the vertex for y=3(x-5)squared+2

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Question 72240This question is from textbook Algebra 1
: Find the vertex for y=3(x-5)squared+2 This question is from textbook Algebra 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In the general equation of a quadratic
y=%28x-h%29%5E2%2Bk Represents a quadratic in "vertex form", in other words the vertex is (h,k). The constant h is the horizontal shift of the vertex and k is the vertical shift of the vertex. For instance if you have y=x%5E2 it looks like this
graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+x%5E2%29The graph of y=x%5E2
Where the vertex is at (0,0). If you want to shift the graph up or down, you simply add or subtract the appropriate units. For instance, to shift 3 units up, just add 3.
graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+x%5E2%2B3%29The graph of y=x%5E2%2B3 (note: h=0 k=3)
For this problem, the shifted units are given to you and all you have to do is find the vertex. If the vertex started at (0,0) and we shifted 2 units up and 5 units to the right then the vertex would be (5,2).
graph%28+300%2C+200%2C+0%2C+10%2C+-5%2C+5%2C+3%2A%28x-5%29%5E2%2B2%29The vertex is the lowest point on the graph