Question 33
Let $a$, $b$ and $c$ be three real numbers. The functions are considered
$$
f(x) = a x^{2} + b x + c \quad \text{y} \quad g(x) = c x^{2} + b x + a
$$
Knowing that
$$
|f(-1)| \leq 1, \quad |f(0)| \leq 1, \quad y \quad |f(1)| \leq 1
$$
prove that if $-1 \leq x \leq 1$, then $|f(x)| \leq 5/4$ and $|g(x)| \leq 2$.
$$
f(x) = a x^{2} + b x + c \quad \text{y} \quad g(x) = c x^{2} + b x + a
$$
Knowing that
$$
|f(-1)| \leq 1, \quad |f(0)| \leq 1, \quad y \quad |f(1)| \leq 1
$$
prove that if $-1 \leq x \leq 1$, then $|f(x)| \leq 5/4$ and $|g(x)| \leq 2$.