Chapter 3.2, Problem 27AYU

To determine

Given quadratic function has a maximum value or minimum value.

Answer to Problem 27AYU

Value of $G\left(0\right)$ is $3.2763$ .

Explanation of Solution

Given information:

Age of mother $x$	Incidence of down syndrone $y$
$33$	$2.4$
$34$	$3.1$
$35$	$4$
$36$	$5$
$37$	$6.7$
$38$	$8.3$
$39$	$10$
$40$	$13.3$
$41$	$16.7$
$42$	$22.2$
$43$	$28.6$
$44$	$33.3$
$45$	$50$

Calculation:

Lets, consider

The linear model representing between dependent variable $G$ and independent variable $h$ is calculated as,

  $G\left(h\right)=-0.0942h+3.2763$

Now, as it given that $G\left(h\right)=0$ or

  $\begin{array}{l}-0.0942h+3.2763=0\\ -0.0942h+3.2763-3.2763=-3.2763\\ -0.0942h=-3.2763\end{array}$

Now, on dividing both sides by $0.0942$

  $\begin{array}{l}\frac{-0.0942h}{0.0942}=\frac{-3.2763}{0.0942}\\ -h=-34.8\\ h=34.8\end{array}$

This interprets that student having his average grade point zero spends $34.8hours$ weekly in playing video games.

Now to calculate $G\left(0\right)$ put $h=0$ in given linear relation.

  $\begin{array}{l}G\left(0\right)=-0.0942h+3.2763\\ =-0.0942\times 0+3.2763\\ =0+3.2763\\ G\left(0\right)=3.2763\end{array}$

So, that interprets that if student does not play videogame for a single moment in a week he or she would have best cumulative average grading point as $3.2763$ among all his classmates.