Question

How do you use the graph to solve `0=6x^2-19x`?

Answer 1

Your equation is `6x^2=19x`

Explanation:

If you arrange the original equation,

`6x^2=19x`

`6x=19`

`x=19/6` or `x=3times1/6` (here your y is zero)

Also when x is zero, you have a solution (when x is zero, your function is zero.

The graph is given below:

graph{(6x^2)-(19x) [-5.33, 5.33, -19, 21]}

Answer 2

`x=0" or "x=19/6`

Explanation:

`"consider the graph of " 6x^2-19x`
graph{6x^2-19x [-10, 10, -5, 5]}

`"the values of x where the graph crosses the x-axis"`
`"are the solutions to"`

`6x^2-19x=0`

`rArrx=0larr" is obvious"`

`" the other root is just over 3"`

`"we can check the solutions exactly using algebra"`

`rarr6x^2-19x=0`

`rArrx(6x-19)=0larr" common factor of x"`

`"equate each factor to zero"`

`6x=0rArrx=0`

`6x-19=0rArrx=19/6larrcolor(red)" exact solution"`

`rArrx=0" or " x=19/6" are the solutions"`