If a(x) = 2x – 4 and b(x) = X + 2, which of the following expressions produces a quadratic function? O (ab)(x) O (a – b)(x)

Question

If a(x) = 2x – 4 and b(x) = X + 2, which of the following expressions produces a quadratic function?
O (ab)(x)
O (a – b)(x)
O (a + b)(x)

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Madeline 2 weeks 2021-11-25T04:18:27+00:00 1 Answer 0

Answers ( )

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    2021-11-25T04:19:52+00:00

    (ab)(x) Produces quadratic function  

    Solution:

    Given that    

    a (x) = 2x – 4  and b(x)  = x + 2

    Need to check which of the expression from given three expression produce a quadratic function. Let us solve each option and check the result.

    (a b)(x)=a(x) \times b(x)=(2 x-4) \times(x+2)

    \begin{array}{l}{=x(2 x-4)+2(2 x-4)} \\\\ {=2 x^{2}-4 x+4 x-8} \\\\ {=2 x^{2}-8}\end{array}

    \Rightarrow \quad(a b)(x)=2 x^{2}-8

    So (ab)(x) produces a quadratic function 2x^2-8.

    \text { 2) }(a-b)(x)=a(x)-b(x)=(2 x-4)-(x+2)

    \begin{array}{l}{=(2 x-4)-(x+2)} \\\\ {=2 x-4-x-2} \\\\ {=x-6}\end{array}

    \Rightarrow(a-b)(x)=x-6

    So (a – b)(x) produces a linear function x – 6.

    \begin{array}{l}{\text { 3) }(a+b)(x)=a(x)+b(x)=(2 x-4)+(x+2)} \\\\ {=(2 x-4)+(x+2)} \\\\ {=2 x-4+x+2} \\\\ {=x-2}\end{array}

    \Rightarrow(a+b)(x)=x-2

    So (a + b)(x) produces a linear function x – 2.

    Hence we can conclude that (ab)(x) produces quadratic function.

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