F(x)=2x^2-14x+24 = 2(x^2-7x+(7/2)^2)-49/2+24 or F(x)= 2(x-7/2)^2-1/2F(x)=2x2−14x+24=2(x2−7x+(72)2)−492+24orF(x)=2(x−72)2−12
Comparing with standard equation F(x)=a (x-h)^2 +f , (h,f)F(x)=a(x−h)2+f,(h,f) being vertex , we get vertex as
h=7/2 , f= -1/2 or (3.5, -0.5)h=72,f=−12or(3.5,−0.5) Axis of symmetry is x=3.5x=3.5
y-intercept can be obtained by putting x=0x=0 in the equation
:.F(x) or y=24
y - intercept is at (0,24)
x-intercept can be obtained by putting F(x) or y=0 in the equation
2(x-7/2)^2-1/2 =0 or 2(x-7/2)^2=1/2 or (x-7/2)^2=1/4 or
(x-7/2)^2= +-sqrt(1/4) :. x =7/2+1/2 =4 and x =7/2 -1/2 =3
x- intercepts are at (3,0) and (4,0) graph{2x^2-14x+24 [-40, 40, -20, 20]} [Ans]
