Question

a road follows the shape of a parabola f(x)=3x2– 24x + 39. A road that follows the function g(x) = 3x – 15 must cross the stream at point A and then again at point B. Bridges must be built at those points. Identify the coordinates where the bridges must be built.

Answer 1

the coordinates where the bridges must be built is
`(3,-6)` and
`(6,3)` .

Explanation:

Here we have , a road follows the shape of a parabola f(x)=3x2– 24x + 39. A road that follows the function g(x) = 3x – 15 must cross the stream at point A and then again at point B. Bridges must be built at those points.We need to find Identify the coordinates where the bridges must be built. Let's find out:

Basically we need to find values of x for which f(x) = g(x) :

⇒
`f(x)-g(x)=0`

⇒
`3x^2- 24x + 39-(3x - 15 ) =0`

⇒
`3x^2- 24x + 39-3x + 15 =0`

⇒
`3x^2- 27x + 54 =0`

⇒
`x^2- 9x + 18 =0`

⇒
`x^2- 6x-3x + 18 =0`

⇒
`x(x- 6)-3(x - 6) =0`

⇒
`(x-3)(x- 6) =0`

⇒
`x=3 , x=6`

Value of g(x) at x = 3 : y=3x -15 = 3(3)-15 = -6

Value of g(x) at x = 6 : y=3x -15 = 3(6)-15 = 3

Therefore , the coordinates where the bridges must be built is
`(3,-6)` and
`(6,3)` .