Question

The graph of g(x) resembles the graph of f(x)=x^2, but it has been changed. Which of these is the equation of g(x)?

Answer 1

A.

Explanation:

Anwer A has the following equation:

`g(x)=(3)/(5)x^2-3`

In this equation, we can calculated the intercept replacing x by 0, as:

`g(x)=(3)/(5)0^2-3=-3`

if this is the answer, the graph of g(x) should be through the point (0,-3) and that happens.

Additionally, the roots of the equations are calculated replacing g(x) by 0 and solving for x, so:

`0=(3)/(5)x^2-3\\x_1=√(5)=2.236\\x_2=-√(5)=-2.236`

It means that the graph of g(x) should be through the points (2.236,0) and (-2.236,0) and that happens too.

So, the answer is A,
`g(x)=(3)/(5)x^2-3`