Chapter 9.2, Problem 43HP

To determine

To formulate function that passes through given points.

Answer to Problem 43HP

The function is $y=x^2-1$

Explanation of Solution

Given information :

The function is of the form $y=a{x}^2+k$

The points given are :- $(-2,3)$ and $(4,15)$ .

Formula used : In a function of the form $y=a{x}^2+k$ , if the values of x and y corresponding to the points it passes through are substituted, two linear equations are obtained with a and k as the unknown variables. These equations can be solved simultaneously to get values of a and k. Calculation :

  $y=a{x}^2+k$

Substituting $x=-2$ and $y=3$ for the point $(-2,3)$ ,

  $3=a{(-2)}^2+k$

Simplifying.

  $4a+k=3$ …(i)

Similarly,

  $y=a{x}^2+k$

Substituting $x=4$ and $y=15$ for the point $(4,15)$ ,

  $15=a{(4)}^2+k$

  $16a+k=15$ …(ii)

Solving equations (i) and (ii) simultaneously;

The values of a and k obtained are,

  $a=1$ and $k=-1$ ;

Therefore substituting the values $a=1$ and $k=-1$ in the function;

  $y=x^2-1$