Answer:
[tex]\large\boxed{\sf f(x) = x^2-6x+9}[/tex]
Step-by-step explanation:
We are here given a graph of a equation and we are interested in finding the equation .
From the given graph we can see that it cuts the x axis at point (3,0) . This graph represents a quadratic function and its two zeroes are 3,3 . We can write the equation using the two zeroes .
Say if the zeroes of the quadratic equation are p and q , then the quadratic equation can be written as ,
[tex]\longrightarrow (x-p)(x-q)=0 [/tex]
And the quadratic function can be written as ,
[tex]\longrightarrow f(x)= k[ (x-p)(x-q)][/tex]
where k is a constant .In this case k = 1 . So we can write the function as ,
[tex]\longrightarrow f(x) = (x-3)(x-3)[/tex]
Distribute ,
[tex]\longrightarrow f(x)= x (x-3)-3(x-3)[/tex]
Simplify by opening the brackets,
[tex]\longrightarrow f(x) = x^2-3x -3x +9 [/tex]
Add like terms,
[tex]\longrightarrow \underline{\underline{f(x) = x^2-6x+9}}[/tex]
And we are done!
