Question

Choose the function rule that matches the given system input with its output.

• A. $\text{y}=25\text{x}-75{\text{x}}^2+34$
• B. $\text{y}=25\text{x}+75{\text{x}}^2-34$
• C. $\text{y}=25\text{x}+75{\text{x}}^2+24$
• D. $\text{y}=25\text{x}+75{\text{x}}^2+34$

Answer 1

The correct option is D $\text{y}=25\text{x}+75{\text{x}}^2+34$

$\text{From the given information, we can observe}$
$\text{that when input is}\frac{2}{5}\text{the output of the function}$
$\text{is 56.}$

Let's analyse the first option:
$\text{Equation given is}:25\text{x}+75{\text{x}}^2+34$

$\text{Substituting x =}\frac{2}{5}\text{we get:}$
$\text{y}=25\times \frac{2}{5}+75(\frac{2}{5}{)}^2+34$
$=10+12+34$
$=56$

This matches with the given output.

Let's analyse the second option:
$\text{Equation given is}:25\text{x}+75{\text{x}}^2+24$

$\text{Substituting x =}\frac{2}{5}\text{we get:}$
$\text{y}=25\times \frac{2}{5}+75(\frac{2}{5}{)}^2+24$
$=10+12+24$
$=46$

This does not match with the given output.

Let's analyse the third option:
$\text{Equation given is}:25\text{x}-75{\text{x}}^2+34$
$\text{Substituting x =}\frac{2}{5}\text{we get:}$
$\text{y}=25\times \frac{2}{5}-75(\frac{2}{5}{)}^2+34$
$=10-12+34$
$=32$

This also does not match with the given output.

Let's analyse the fourth option:
$\text{Equation given is}:25\text{x}+75{\text{x}}^2-34$
$\text{Substituting x =}\frac{2}{5}\text{we get:}$
$\text{y}=25\times \frac{2}{5}+75(\frac{2}{5}{)}^2-34$
$=10+12-34$
$=-12$

This also does not match with the given output.

So, the first option is the correct one.