Question

How do you solve `1/3x^2 - 3=0` by graphing?

Answer 1

Refer the Explanation section

Explanation:

Given -

`1/3 x^2-3=0`

We shall have it as -

`y=1/3 x^2-3`

To graph the function, we must have the range of x values the includes solutions.

Find the two x-intercepts first

At `y=0; 1/3x^2-3=0`

`x^2=-=3 xx 3/1=9`

`x=+-sqrt9`
`x=3`
`x=-3`

The curve cuts the x-axis at `(3,0);(-3,0)`

Now take `x` values ranging from `5` to `-5`
Find the corresponding `y` values.

Then plot these values on a graph sheet.

Answer 2

Plot the graph of `f(x) = 1/3x^2-3`. Solutions for `x` are found where `f(x)` intercepts the `x-`axis. `x=+-3`

Explanation:

The graph of `f(x) = 1/3x^2-3` is shown below.

graph{1/3x^2-3 [-7.023, 7.024, -3.51, 3.513]}

From this graph we can observe the `f(x)=0` for `x=+-3`

Hence this is the answer to this question.

We can, of course, solve the equation algebraically to prove this observation.

`1/3x^2-3=0 -> 1/3x^2 = 3`

`:.x^2=3xx3 = 9`

`x=sqrt9 =+-3`