Question

Which polynomial function could be represented by the graph below?

f(x) = x2 – 6x + 8
f(x) = 3x2 – 18x + 24
f(x) = x2 + 6x + 8
f(x) = 3x2 + 18x + 24

Answer 1

f(x) = 3x^2 – 18x + 24

Explanation:

I put it into Desmos

Answer 2

`f(x)=3x^2-18x+24`

Explanation:

we are given a graph

we can see that graph is of parabola

so, the function will be quadratic in nature

Firstly, we can identify zeros

zeros are x=2 and x=4

now, we can set up function

`f(x)=a(x-2)(x-4)`

now, we can select anyone point and find 'a'

at x=3 , y=-3

we can use it and find 'a'

`-3=a(3-2)(3-4)`

`a=3`

now, we can plug it back

and we get

`f(x)=3(x-2)(x-4)`

we can multiply it

and we get

`f(x)=3x^2-18x+24`