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(B) Since $f(x)$ is a second degree polynomial and $f(-3) = 0$,we can write $f(x) = a(x + 3)(x - k)$ for some constant $a$ and root $k$.Given $f(x) \g

Vedclass · Accepted Answer

$72$

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(B) Since $f(x)$ is a second degree polynomial and $f(-3) = 0$,we can write $f(x) = a(x + 3)(x - k)$ for some constant $a$ and root $k$.Given $f(x) \geq 0$ for all $x \in R$,the graph of $f(x)$ must touch the $x$-axis at exactly one point,meaning it has a double root at $x = -3$. Thus,$k = -3$.So,$f(x) = a(x + 3)^2$.Using the condition $f(0) = 18$:$a(0 + 3)^2 = 18$$9a = 18$$a = 2$.Therefore,$f(x) = 2(x + 3)^2$.Now,calculating $f(3)$:$f(3) = 2(3 + 3)^2 = 2(6)^2 = 2 	imes 36 = 72$.

If $f(x)$ is a second degree polynomial such that $f(x) \geq 0$ for all $x \in R$,$f(-3) = 0$,and $f(0) = 18$,then find $f(3)$.

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