#f(x) = -9x^2 +7x +6 ; a= -9 , b=7 , c=6 , # comparing with standard equation #f(x)=ax^2+bx+c #.
Vertex (x-ordinate) #=-b/(2a) = -7/-18=7/18 ~~0. 39(2dp)#
Vertex (y-ordinate) #f(x)=-9*7^2/18^2+7* 7/18 +6 ~~ 7.36(2dp)#
So Vertex is at #(0.39 , 7.36)#
y-intercept can be obtained by putting #x=0# in the equation , i.e #f(x)= -9*0 +7*0 +6 =6 :. # y-intercept is at #(0,6)#
x-intercept can be obtained by putting #f(x)=0# in the equation , i.e
#0 = -9x^2 +7x +6 #
# :. x= - b/(2a) +- sqrt(b^2-4ac)/(2a) #
#:.x = -7/-18 +- sqrt (49 - 4 * -9 *6)/-18 =7/18 +- sqrt265/ -18 #
#:. x ~~ - 0.52(2dp) , x ~~ 1.29 (2dp)#
x-intercept is at # (1.29,0) and ( -0.52,0)# graph{-9x^2+7x+6 [-20, 20, -10, 10]}[Ans]
