SOLUTION: Let P= (x,y) be a point on the graph on y=sqrt(x) or y=x^1/2 (not sure how to express the square root of x here) a). Express the distance d from P to the point (1,0) as a funct

Algebra ->  Points-lines-and-rays -> SOLUTION: Let P= (x,y) be a point on the graph on y=sqrt(x) or y=x^1/2 (not sure how to express the square root of x here) a). Express the distance d from P to the point (1,0) as a funct      Log On


   



Question 953374: Let P= (x,y) be a point on the graph on y=sqrt(x) or y=x^1/2 (not sure how to express the square root of x here)
a). Express the distance d from P to the point (1,0) as a function of x.
b). graph in your calculator to find the value(s) of x where d is the smallest.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Either way is correct.
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y=sqrt%28x%29
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Using the distance formula,
d%5E2=%28x-1%29%5E2%2B%28y-0%29%5E2
d%5E2=%28x-1%29%5E2%2By%5E2
d%5E2=%28x-1%29%5E2%2Bx
d%5E2=x%5E2-2x%2B1%2Bx
d%5E2=x%5E2-x%2B1
d=sqrt%28x%5E2-x%2B1%29
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Algebraically, the function is minimized when the argument value is minimized.
y=x%5E2-x%2B1
y=x%5E2-x%2B1%2F4%2B1-1%2F4
y=%28x-1%2F2%29%5E2%2B3%2F4
Since it's in vertex form, the value is the minimum and occurs at x=1%2F2
y=3%2F4
d%5Bmin%5D=sqrt%283%2F4%29
d%5Bmin%5D=sqrt%283%29%2F2