Question 976873
y= -x^2+3x+4 is in the quadratic form y= ax2 + bx + c
The vertex (h, k) is found by computing h = –b/2a, and then evaluating y at h to find k.
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h = –b/2a = –(3)/2(1) = –3/2 or -1 1/2, this is one of our vertex points.
Now we can find k by evaluating y at h= -3/2:
k= (-3/2)^2+3(-3/2)+4
= 9/4 -9/2 + 4
=9/4 - 18/4 + 16/4 
=  (9-18+16)/4
= 7/4 or 1 3/4
The vertex is at (-1 1/2, 1 3/4)