Question

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

Answer 1

$(ab)(x)$ 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.