Question

.Use the graph of y=x^2 - 6x + 9 to solve the equation x^2 - 6x = -9

Answer 1

See the attached graph from which we obtain x = 3 as the only solution for the given equation.

Explanation:

Notice that the equation
`x^2-6x=-9` is the same equation as when y = 0 in the function
`y = x^2-6x+9`, since when y=0 we have:

`y = x^2-6x+9\\0 = x^2-6x+9\\-9=x^2-6x`

Then what we need to find is for which values of "x" in the graph of y = x^2-6x+9, the graph touches or crosses the x-axis (that is when y=0)

We graph the given function in the x-y coordinate system and find where it renders zero for "y" (see attached graph).

We see that there is only one point of contact with the x-axis at x = 3