Question

Q(a+1) - 2q(a) if q(x) = x²+3x+4​

Answer 1

$q(x) = {x}^{2} + 3x + 4$

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Step(1)

To find q(a) we just need to put a instead of x in q(x) function.

Let's do it...

$q(a) = {a}^{2} + 3a + 4$

Multiply sides by -2 :

$- 2q(a) = - 2( {a}^{2} + 3a + 4)$

$- 2q(a) = - 2 {a}^{2} - 6a - 8$

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Step (2)

To find q(a+1) we just need to put a+1 instead of x in q(x) function.

Let's do it...

$q(a + 1) = ({a + 1})^{2} + 3(a + 1) + 4$

$q(a + 1) = {a}^{2} + 2a + 1 + 3a + 3 + 4$

$q(a + 1) = {a}^{2} + 5a + 8$

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Step (3)

$q(a + 1) - 2q(a) =$

${a}^{2} + 5a + 8 - 2 {a}^{2} - 6a - 8 =$

$- {a}^{2} - a = - a(a + 1)$

And we're done.

Thanks for watching buddy good luck.

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