Question

Which function matches this graph?

Answer 1

Answer:

$\large\boxed{\sf f(x) = x^2-6x+9}$

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 ,

$\longrightarrow (x-p)(x-q)=0$

And the quadratic function can be written as ,

$\longrightarrow f(x)= k[ (x-p)(x-q)]$

where k is a constant .In this case k = 1 . So we can write the function as ,

$\longrightarrow f(x) = (x-3)(x-3)$

Distribute ,

$\longrightarrow f(x)= x (x-3)-3(x-3)$

Simplify by opening the brackets,

$\longrightarrow f(x) = x^2-3x -3x +9$

Add like terms,

$\longrightarrow \underline{\underline{f(x) = x^2-6x+9}}$

And we are done!