Question

How do you graph `f(x) = 2x^2 – 2` by plotting points?

Answer 1

`"see explanation"`

Explanation:

`"select values of x and substitute into equation for values of y"`

`"the x-intercepts can be found by equating f(x) to zero"`

`rArr2x^2-2=0rArr2(x^2-1)=0`

`rArr2(x-1)(x+1)=0`

`rArrx=-1 , x=1larrcolor(red)" x-intercepts"`

`f(color(red)(0))=0-2=-2rArr(0,-2)larrcolor(red)" y-intercept"`

`f(color(red)(2))=8-2=6rArr(2,6)`

`f(color(red)(-2))=8-2=6rArr(-2,6)`

Plot the x / y intercepts plus the other 2 points. Draw a smooth curve through them for the graph.
graph{2x^2-2 [-10, 10, -5, 5]}