To find the [tex]\( x \)[/tex]-intercepts of the given quadratic function, we need to understand that the [tex]\( x \)[/tex]-intercepts occur where the function crosses the [tex]\( x \)[/tex]-axis. These points are also known as the roots or zeros of the function, and they are found by setting the function equal to zero and solving for [tex]\( x \)[/tex].
Given the factors of the quadratic function, [tex]\((x+2)\)[/tex] and [tex]\((x-9)\)[/tex], we can find the [tex]\( x \)[/tex]-intercepts as follows:
1. Set each factor equal to zero and solve for [tex]\( x \)[/tex]:
- For the factor [tex]\((x+2)\)[/tex]:
[tex]\[
x+2 = 0
\][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[
x = -2
\][/tex]
- For the factor [tex]\((x-9)\)[/tex]:
[tex]\[
x-9 = 0
\][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[
x = 9
\][/tex]
2. The solutions to these equations tell us where the function crosses the [tex]\( x \)[/tex]-axis. Hence, the [tex]\( x \)[/tex]-intercepts of the function are:
[tex]\[
(-2, 0) \quad \text{and} \quad (9, 0)
\][/tex]
Thus, the correct answer is:
[tex]\[ \text{B. } (-2,0) \text{ and } (9,0) \][/tex]
