Consider the polynomials $f(x) = ax^2 + bx + c$, where $a 0, b, c$ are real, $g(x) = -2x$. If $f(x)$ cuts the x-axis at $(-2, 0)$ and $g(x)$ passes through $(a, b)$, then the minimum…

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Consider the polynomials $f(x) = ax^2 + bx + c$, where $a > 0, b, c$ are real, $g(x) = -2x$. If $f(x)$ cuts the x-axis at $(-2, 0)$ and $g(x)$ passes through $(a, b)$, then the minimum value of $f(x) + 9a + 1$ is

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B - 1. g passes through (a,b): b=-2a. f(-2)=0: 4a-2b+c=0 -> 8a+c=0 -> c=-8a. f = a(x^2-2x-8), minimum at x=1 equals -9a. So min of f+9a+1 = 1.

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A - 0

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C - 2

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D - 3

Consider the polynomials \(f(x) = ax^2 + bx + c\), where \(a > 0, b, c\) are real, \(g(x) = -2x\). If \(f(x)\) cuts the x-axis at \((-2, 0)\) and \(g(x)\) passes through \((a, b)\), then the minimum…

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