Question 817880
 <pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi,
Using the vertex form of a parabola, {{{y=a(x-h)^2 +k}}} 
where(h,k) is the vertex
P(x) = -3x^2 + 24x - 46   |Completing the Square to find vertex form
P(x) = -3(x^2 -8x +16) +48  - 46
P(x) = -3(x-4)^2 + 2   V(4,2) 
 0 = -3(x-4)^2 + 2 
 (x-4)^2 = 2/3,  x = 4 ± {{{sqrt(2/3)}}} 
{{{drawing(300,300,   -6, 6, -6, 6, grid(1), 
circle(4, 2,0.3),
circle(4 + sqrt(2/3), 0,0.3),
circle(4-sqrt(2/3), 0,0.3),

graph( 300, 300, -6, 6, -6, 6,0, -3x^2 + 24x - 46     ))}}}