Question

Question #f37a1

Answer 1

Vertex is at `(3.5, -0.5)` , axis of symmetry is `x=3.5`,
y-intercept is at `(0,24)`, x-intercepts are at `(3,0) and (4,0)`

Explanation:

`F(x)=2x^2-14x+24 = 2(x^2-7x+(7/2)^2)-49/2+24 or F(x)= 2(x-7/2)^2-1/2`
Comparing with standard equation `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)` Axis of symmetry is `x=3.5`

y-intercept can be obtained by putting `x=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]