Question 1173301
<pre><font face = "consolas" color = "indigo" size = 4><b>
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 = a(x+1)(x-7)  |Using P(5,6), 6 = a(-12) , a = (-1/2)
 y =-1/2(x^2 - 6x - 7)  0r by taking the -7 outside the parenthesis
 y = -1/2(x^2-6x) +7/2  Completing the Square
  y = -1/2(x^2-6x +9  -9) +7/2    |taking the -9 outside the parenthesis
 y = -1/2(x-3)^2 +9/2 + 7/2 0r
 y = -1/2(x-3)^2  + 8     V(3,8) & crosses x-axis at x = -1  and x=7
Wish You the Best in your Studies. 
{{{drawing(300,300,    -10,10,-10,10,  blue(line(3,100, 3,-100))  ,  
 grid(1),
circle(3, 8,0.4),
circle(-1, 0,0.4),
circle(7, 0,0.4),
graph( 300, 300, -10,10,-10,10,0,  (-1/2)x^2+3x +7/2  ))}}}