Question

given the function $f(x) = 2x^2 + 7x - 2$. 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 $f(x)$

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

Step2: Simplify to find $f(0)$

$f(0)=0+0-2=-2$

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

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

Step4: Simplify to find $f(2)$

$f(2)=2(4)+14-2=8+14-2=20$

Step5: Substitute $x=-2$ into $f(x)$

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

Step6: Simplify to find $f(-2)$

$f(-2)=2(4)-14-2=8-14-2=-8$

Step7: Substitute $x=x+1$ into $f(x)$

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

Step8: Expand and simplify $f(x+1)$

$f(x+1)=2(x^2+2x+1)+7x+7-2=2x^2+4x+2+7x+7-2=2x^2+11x+7$

Step9: Substitute $x=-x$ into $f(x)$

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

Step10: Simplify to find $f(-x)$

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

Answer:

$f(0)=-2$
$f(2)=20$
$f(-2)=-8$
$f(x+1)=2x^2+11x+7$
$f(-x)=2x^2-7x-2$