y=3x^2-18x+4 = 3(x^2-6x)+4 = 3(x^2-6x+9) -27 +4 y=3x2−18x+4=3(x2−6x)+4=3(x2−6x+9)−27+4 or
y=3(x-3)^2 -23 y=3(x−3)2−23 Comparing with vertex form of equation
y=a(x-h)^2+k ; (h,k)y=a(x−h)2+k;(h,k) being vertex we find here h=3 ; k=-23h=3;k=−23
So vertex is at (3,-23)(3,−23) , y-intercept can be found by putting x=0x=0 in the equation :.y=4 ; y-intercept is at (0,4)
x-intercept can be found by putting y=0 in the equation .
:. 3(x-3)^2 -23 =0 or 3(x-3)^2 = 23 or (x-3)^2 =23/3 or
(x-3) = +- sqrt(23/3) or x = 3 +- sqrt(23/3) :. x ~~ 5.77(2dp) and x ~~0.23(2dp)
x-intercepts are at (0.23,0) and (5.77,0)
graph{3x^2-18x+4 [-80, 80, -40, 40]} [Ans]
