Question

How do you identify the important parts of `f(x)= 2x^2 - 11` to graph it?

Answer 1

Any quadratic equation of form `y=ax^2+bx+c` has a parabola graph.

If a is positive (like here a = 2) then the arms go up.

In this case, c = -11 and represents the y-intercept.

The roots or x-intercepts of the equation are when y = 0, So in this case when `2x^2-11=0 => x= + or -sqrt(11/2)`

The axis of symmetry is at `x=(-b)/(2a)=0` in this case.

Then you can combine it all to draw the graph.

graph{2x^2-11 [-25.66, 25.65, -12.83, 12.83]}