Question

How do you solve `2x^2-7x+3>=0` by graphing?

Answer 1

`x<=1/2" or " x>=3`

Explanation:

Factorise the quadratic and find the roots.

`rArr(2x-1)(x-3)=0`

`rArr"roots are "x=1/2" and " x=3`

`x=0toy=3rArr(0,3)`

`"coefficient of " x^2>0" thus" uu`

With this information we can sketch the function.
graph{2x^2-7x+3 [-10, 10, -5, 5]}

To solve `2x^2+7x-3>=0` Consider the region above and including the x-axis.

Above x-axis to the left of `1/2` and right of 3

`rArrx<=1/2" or " x>=3`