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What is the leftmost point on the curve x = y^2 - y + 2?

 May 10, 2020
 #1
avatar+1543 
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Graphing gives me (1.75, 0.5)

 

I used Apple's grapher since I was too lazy LOL

 May 10, 2020
edited by hugomimihu  May 10, 2020
 #2
avatar+21000 
+1

This is the equation of a horizontal parabola whose vertex is on the left side and opens to the right.

 

To find the vertex, complete the square:

 

               x  =  y2 - y + 2

          x - 2  =  y2 - y

   x - 2 + ¼  =  y2 - y + ¼                          (complete the square)

       x - 7/4  =  (y - ½)2

 

The vertex is  (7/4, 1/2)

 May 10, 2020

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