Question

Graphing Polynomial Functions

Answer 1

Let's assume

'a' , 'b' are zeros

so, we will find total zeros from graph

We can  curve touches x-axis

Let's assume it touches at x=b

so, there would be two zeros at x=b

it also crosses origin

so, another zero is at x=0

it crosses x-axis one more time

Let's assume that zeros at x=a

so, we have got four zeros

x=a,0,b,b

now, we can set up function

$f(x)=(x-0)(x-a)(x-b)(x-b)$

we can also write as

$f(x)=x(x-a)(x-b)^2$.................Answer