Question #0be35

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Answer 1 · 2017-05-04T21:27:42

#y=-x^2+10x-23#

Your answer is correct, I'm not sure why that website says the answer is wrong...

We have the vertex #(5,2)#, and the parabola has a negative #a# value because the graph is convex.

Looking at the other point (4,1), we can tell that the #a# value is equal to #-1# because of the slope, but just to confirm:

Vertex form: #color(blue)(y=a(x-h)+k)#
#y=a(x-5)^2+2#

Expand:
#y=a(x^2-10x+25)+2#

Try the point #(4,1)# to determine the value of #a#
#1=a(16-40+25)+2#
#1=a+2#
#a=-1#

#y=-(x^2-10x+25)+2#

#y=-x^2+10x-25+2#

#y=-x^2+10x-23#