Problem 3 · Cancel even terms at opposite inputs · 3 points
Made by AI and not reviewed by a real person.
A quadratic function gives f(−2)=10 and f(2)=−2. What is f(−3)−f(3)?
- 0
- −18
- 12
- −12
- 18
Show a hint
- Compare the outputs at opposite inputs: which parts of a quadratic stay the same, and which change sign?
- Write f(x)=ax²+bx+c. Subtracting the outputs at opposite inputs makes two terms disappear.
Show the answer and solution
Answer: E — 18
For f(x)=ax²+bx+c, we have f(−2)−f(2)=−4b=10−(−2)=12, so b=−3. Thus f(−3)−f(3)=−6b=18. The tempting −18 reverses the subtraction or loses a negative sign.