Question

I can't remember how to do this. I need help with this.

How many roots do the functions have in common?
f(x)=x^2-9

Answer 1

one root common that's -3

Explanation:

use desmos

Answer 2

The quadratic function
`\(f(x) = x^2 - 9\)` has two roots in common with the x-axis:
`\(x = 3\)` and
`\(x = -3\)`. These are the points where the function equals zero.

The function
`\( f(x) = x^2 - 9 \)` can be factored as
`\( f(x) = (x - 3)(x + 3) \)`. The roots, or values of x that make f(x) equal to zero, are
`\( x = 3 \)` and
`\( x = -3 \)`. These are the points where the graph intersects the x-axis.

The factors
`\( (x - 3) \)` and
`\( (x + 3) \)` represent the linear expressions corresponding to these roots.

Therefore, the function has two roots in common with the x-axis, and these roots are
`\( x = 3 \)` and
`\( x = -3 \)`. These points are essential in understanding the behavior and intersections of the quadratic function
`\( f(x) \)`.