Which function matches this graph? f(x)=x2−3f ( x ) = x 2 − 3
f(x)=x2+9f x = x 2 + 9

f(x)=x2−6x+9f ( x ) = x 2 − 6 x + 9
f(x)=x2+6x+9f ( x ) = x 2 + 6 x + 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 ,

And the quadratic function can be written as ,

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

Distribute ,

Simplify by opening the brackets,

Add like terms,

And we are done!