Question

given the function $f(x) = 6x^2 + 7x - 7$. calculate the following values:
$f(0) = $
$f(2) = $
$f(-2) = $
$f(x+1) = $
$f(-x) = $
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Explanation:

Step1: Substitute $x=0$ into $f(x)$

$f(0)=6(0)^2 + 7(0) - 7 = 0 + 0 - 7$

Step2: Substitute $x=2$ into $f(x)$

$f(2)=6(2)^2 + 7(2) - 7 = 6(4) + 14 - 7 = 24 + 14 - 7$

Step3: Substitute $x=-2$ into $f(x)$

$f(-2)=6(-2)^2 + 7(-2) - 7 = 6(4) - 14 - 7 = 24 - 14 - 7$

Step4: Substitute $x+1$ into $f(x)$

$f(x+1)=6(x+1)^2 + 7(x+1) - 7 = 6(x^2+2x+1) + 7x+7 - 7 = 6x^2+12x+6+7x$

Step5: Substitute $-x$ into $f(x)$

$f(-x)=6(-x)^2 + 7(-x) - 7 = 6x^2 -7x -7$

Answer:

$f(0) = -7$
$f(2) = 31$
$f(-2) = 3$
$f(x+1) = 6x^2+19x+6$
$f(-x) = 6x^2-7x-7$