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If the factors of a quadratic function are (x+2) and (x-9), what are the x-intercepts of the function?
OA. (-9,0) and (2,0)
O B. (-2,0) and (9,0)
О с.
(2,0) and (9,0)
O D. (-9,0) and (-2,0)
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Verified Answer :

GinnyAnswer

To determine the x-intercepts of a quadratic function when its factors are given, we set each factor equal to zero and solve for \(\( x \)\).

The factors of the quadratic function are:
\(\[ (x + 2) \text{ and } (x - 9) \]\)

Step 1: Set each factor equal to zero.
- For the first factor: \(\( x + 2 = 0 \)\)

Step 2: Solve for \(\( x \)\).
- \(\( x + 2 = 0 \)\)
- Subtract 2 from both sides: \(\( x = -2 \)\)

So, one x-intercept is \(\( (-2, 0) \)\).

Step 3: Set the second factor equal to zero.
- For the second factor: \(\( x - 9 = 0 \)\)

Step 4: Solve for \(\( x \)\).
- \(\( x - 9 = 0 \)\)
- Add 9 to both sides: \(\( x = 9 \)\)

So, the other x-intercept is \(\( (9, 0) \)\).

Therefore, the x-intercepts of the quadratic function are:
\(\[ (-2, 0) \text{ and } (9, 0) \]\)

The correct answer is:
\(\[ \text{Option B:} (-2,0) \text{ and } (9,0) \]\)