Respuesta :

hnori22003

[tex]q(x) = {x}^{2} + 3x + 4 [/tex]

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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...

[tex]q(a) = {a}^{2} + 3a + 4 [/tex]

Multiply sides by -2 :

[tex] - 2q(a) = - 2( {a}^{2} + 3a + 4) [/tex]

[tex] - 2q(a) = - 2 {a}^{2} - 6a - 8 [/tex]

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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...

[tex]q(a + 1) = ({a + 1})^{2} + 3(a + 1) + 4 \\ [/tex]

[tex]q(a + 1) = {a}^{2} + 2a + 1 + 3a + 3 + 4 \\ [/tex]

[tex]q(a + 1) = {a}^{2} + 5a + 8 [/tex]

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Step (3)

[tex]q(a + 1) - 2q(a) = [/tex]

[tex] {a}^{2} + 5a + 8 - 2 {a}^{2} - 6a - 8 = \\ [/tex]

[tex] - {a}^{2} - a = - a(a + 1)[/tex]

And we're done.

Thanks for watching buddy good luck.

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abidemiokin

The expression for q(a+1) - 2q(a) is -a² - a

Given the expression q(x) = x²+3x+4​

First, we need to get the function q(a+1)

q(a+1) =  (a+1)²+3(a+1)+4​

Expand

q(a+1) = a² + 2a + 1 + 3a + 3 + 4

q(a+1) = a² + 5a + 8

For the function q(a)

q(a) = a²+3a+4​

2q(a) = 2(a²+3a+4​)

2q(a)= 2a² + 6a + 8

Taking the difference:

q(a+1) - 2q(a) = a² + 5a + 8 - ( 2a² + 6a + 8)

q(a+1) - 2q(a)  = a² + 5a + 8 -  2a² - 6a - 8

q(a+1) - 2q(a)  = -a² - a

Hence the expression for q(a+1) - 2q(a) is -a² - a

Learn more here: https://brainly.com/question/17581815

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