Question 1173304
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Hi  
Note: the vertex form of a Parabola opening up(a>0) or down(a<0), 
{{{y=a(x-h)^2 +k}}} 
where(h,k) is the vertex  and  x = h  is the Line of Symmetry.
 y= -x^2+10x+7   0r
  y= -(x^2-10x) + 7  
Completing the Square  
 y= -(x^2-10x +25  -25)+ 7  0r by taking the -25 outside the parenthesis
 y = -(x^2-5)   + 25 +7 
  y = -(x^2-5) + 32    
 V(5,32)  and line of Symmetry is x = 5
Maximum at P(5,32)
Wish You the Best in your Studies.  
{{{drawing(300,300,    -50,50,-50,50,  blue(line(5,100, 5,-100))  ,  
 grid(1),
circle(5, 32,1.0),
circle(-1, 0,0.4),
circle(7, 0,0.4),
graph( 300, 300, -50,50,-50,50,0,  -x^2+10x+7, -3x^2+12x-17 ))}}}
As to: y=-3x^2+12x-17 Completing the Square: Same Steps as Above 
y = -3(x-2)^2 -5  V(2,-5)max  and Line of Symmetry is x = 2