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

Step-by-step 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

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

at x=3 , y=-3

we can use it and find 'a'

now, we can plug it back

and we get

we can multiply it

and we get

f(x) = 3x^2 – 18x + 24

Step-by-step explanation:

I put it into Desmos

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

addition

step-by-step explanation: