Question

given the function $f(x) = 8x^2 + 3x - 7$. calculate the following values:
$f(0) = -7$
$f(2) = 31$
$f(-2) = -45$
$f(x + 1) = $
$f(-x) = $

Explanation:

Step1: Substitute $x+1$ into $f(x)$

$f(x+1)=8(x+1)^2+3(x+1)-7$

Step2: Expand $(x+1)^2$ and simplify

$f(x+1)=8(x^2+2x+1)+3x+3-7$
$f(x+1)=8x^2+16x+8+3x+3-7$
$f(x+1)=8x^2+19x+4$

Step3: Substitute $-x$ into $f(x)$

$f(-x)=8(-x)^2+3(-x)-7$

Step4: Simplify the expression

$f(-x)=8x^2-3x-7$

Answer:

$f(x+1)=8x^2+19x+4$
$f(-x)=8x^2-3x-7$