To determine the x-intercepts of a quadratic function when its factors are given, we set each factor equal to zero and solve for [tex]\( x \)[/tex].
The factors of the quadratic function are:
[tex]\[ (x + 2) \text{ and } (x - 9) \][/tex]
Step 1: Set each factor equal to zero.
- For the first factor: [tex]\( x + 2 = 0 \)[/tex]
Step 2: Solve for [tex]\( x \)[/tex].
- [tex]\( x + 2 = 0 \)[/tex]
- Subtract 2 from both sides: [tex]\( x = -2 \)[/tex]
So, one x-intercept is [tex]\( (-2, 0) \)[/tex].
Step 3: Set the second factor equal to zero.
- For the second factor: [tex]\( x - 9 = 0 \)[/tex]
Step 4: Solve for [tex]\( x \)[/tex].
- [tex]\( x - 9 = 0 \)[/tex]
- Add 9 to both sides: [tex]\( x = 9 \)[/tex]
So, the other x-intercept is [tex]\( (9, 0) \)[/tex].
Therefore, the x-intercepts of the quadratic function are:
[tex]\[ (-2, 0) \text{ and } (9, 0) \][/tex]
The correct answer is:
[tex]\[ \text{Option B:} (-2,0) \text{ and } (9,0) \][/tex]
