Question

The graph of F(x), show below, resemble the graph of G(x) = x^2 but it has been charged somewhat. which of the following could be the equation of F(x)?

Answer 1

x-axisThe given function is as follows, I am gonna also write the standard form of it.!

`G(x)=x^2\rightarrow sandard\text{ }\rightarrow G(x)=a\cdot(x\pm b)^2\pm c`

Where a, b, c are constants that adjust the apparent look and position of the function.

a changes width of the function, b translates or moves function along the x-axis, and finally, c translates or moves the function along the y-axis.

Now the function in red has the following properties:

It is shifted -2 in x and -2 in y and it is skewed or narrowed (its width is reduced )

Keeping these in mind, for x translation to go 2 units in a negative direction the 'b' has to be +2, and similarly, for y translation, the c has to be -2.

At this point keeping these values in mind, option c matches with the f(x).

`f(x)=3(x+2)^2-2`