Question

Option D is the graph has an intercept at (0,0) . Option E is the graph is increasing on the interval X <0 and decreasing on the interval x>0. Option F is the graph has a relative maximum at (0,0) .Option G is the graph is symmetric with respect to the Y axis I just wasn’t able to fit them all in I just need a brief explanation with the answer

Answer 1

First, notice that the graph is a parabolla, then, the function is a quadratic function.

This means that it has the following form:

$f(x)=ax^2+bx+c$

from this, we can state the following:

1.- The domain of the function is the set of all real numbers, since it is a polynomial function

2;- The range of the function is the set of all nonnegative real numbers, since its a quadratic function.

3.- The vertex of the parabolla is located at the point (0,0), which is an intercept of the graph

4.- The graph is symmetric with respect to the y-axis