Chapter 4.9, Problem 22E

To determine

To calculation: The equation representing A, B and C.

Answer to Problem 22E

The required equation is $y=3\left(x+6\right)\left(x-1\right)\left(x-3\right)$ .

Explanation of Solution

Given information:

The given statement is:

The distance from A to B is less than or equal to the distance from A to C.

Formula used:

Equation of cubic root:

  $y=a\left(x-A\right)\left(x-B\right)\left(x-C\right)$

Calculation:

Consider the equation of cubic root:

  $y=a\left(x-A\right)\left(x-B\right)\left(x-C\right)$

Consider the x values from the given graph

  $A=2$

  $B=3$

  $C=6$

  $a=1$

Substitute the above values in the equation of cube root $y=a\left(x-A\right)\left(x-B\right)\left(x-C\right)$

  $y=a\left(x-2\right)\left(x-3\right)\left(x-6\right)$

Hence, the required equation is $y=a\left(x-2\right)\left(x-3\right)\left(x-6\right)$ .