do the functions have the same concavity?\n$f(x)=-3x^{2}+12x - 32$\nchoose 1 answer:\na yes, $f$ and $g$ are…

do the functions have the same concavity?\n$f(x)=-3x^{2}+12x - 32$\nchoose 1 answer:\na yes, $f$ and $g$ are both concave down.\nb yes, $f$ and $g$ are both concave up.\nc no, $f$ is concave up and $g$ is concave down.\nd no, $f$ is concave down and $g$ is concave up.

do the functions have the same concavity?\n$f(x)=-3x^{2}+12x - 32$\nchoose 1 answer:\na yes, $f$ and $g$ are both concave down.\nb yes, $f$ and $g$ are both concave up.\nc no, $f$ is concave up and $g$ is concave down.\nd no, $f$ is concave down and $g$ is concave up.

Answer

Explanation:

Step1: Recall concavity rule for quadratic functions

For a quadratic function $y = ax^{2}+bx + c$, if $a>0$, the function is concave - up; if $a < 0$, the function is concave - down. For $f(x)=-3x^{2}+12x - 32$, $a=-3<0$, so $f(x)$ is concave down.

Step2: Analyze the graph of $y = g(x)$

The graph of $y = g(x)$ opens downwards. A function that opens downwards is concave down.

Answer:

A. Yes, $f$ and $g$ are both concave down.