Question

final milestone
consider the function $f(x) = -x^2 - 4x + 5$.
use it to find $f(2)$, $f(-3)$, and $f(a - 4)$.

$f(2)= - 7$
$f(-3)=8$
$f(a - 4)= - a^2+4a+5$

$f(2)= - 7$
$f(-3)=2$
$f(a - 4)= - a^2-4a+41$

$f(2)= - 7$
$f(-3)=8$
$f(a - 4)= - a^2+4a-15$

$f(2)= - 7$
$f(-3)=26$

Explanation:

Step1: Calculate $f(2)$

Substitute $x=2$ into $f(x)$:

$$\begin{align*} f(2)&=-(2)^2 -4(2)+5\\ &=-4-8+5\\ &=-7 \end{align*}$$

Step2: Calculate $f(-3)$

Substitute $x=-3$ into $f(x)$:

$$\begin{align*} f(-3)&=-(-3)^2 -4(-3)+5\\ &=-9+12+5\\ &=8 \end{align*}$$

Step3: Calculate $f(a-4)$

Substitute $x=a-4$ into $f(x)$:

$$\begin{align*} f(a-4)&=-(a-4)^2 -4(a-4)+5\\ &=-(a^2-8a+16)-4a+16+5\\ &=-a^2+8a-16-4a+21\\ &=-a^2+4a+5 \end{align*}$$

Answer:

A. $f(2) = - 7$, $f(-3) = 8$, $f(a - 4) = -a^2 + 4a + 5$