Quadratic Equations
Quadratic Equations
Allen Star Batch
Grade 11
Question:
Given that $a > 0$, $|ax^2 + bx + c| \leq 1$ if $-1 \leq x \leq 1$, $a, b, c \in \mathbb{R}$ and $ax + b$ has its maximum value $2$ when $-1 \leq x \leq 1$. Then $b =$
Step-by-Step Solution
Key Concept: Multiple constraints on function values and extrema over-determine the coefficients, allowing unique recovery.
Same as question 13—determining the quadratic $f(x) = ax^2 + bx + c$ from given conditions yields $a = 2$, $b = 0$, $c = -1$.
Correct Answer: 4