Question

How do you solve the equation `-x^2 + 14x - 49 = 0` by graphing the related function?

Answer 1

`x=7`

Explanation:

`-x^2+14x-49=0`
`x^2-14x+49=0`
`(x-7)^2=0`

This is a `y=x^2` parabola that has been shifted to the right by 7 units.

graph{x^2 [-10, 10, -5, 5]}
Above is `y=x^2`

graph{(x-7)^2 [-10, 10, -5, 5]}
Above is `y=(x-7)^2`

Hence, solving for `(x-7)^2=0`, the only possible answer is `x=7`