How do I find the zeroes of this function?

Question

f(x) = 25x² + 60x + 36

 

and how do I find the maximum or minimum value of f(x).

Answer 1

To find the zeroes of this function, we set f(x) = 0.

 

25x² + 60x + 36 = 0

 

 

Factor the equation, if possible.

 

(5x + 6)(5x + 6) = 0

 

 

Set the factors equal to zero.

 

5x + 6 = 0

 

5x = -6

 

  x = -6/5

  x = -1.2

 

 

To find the maximum or minimum of f(x), we put the function in vertex form.  Since we have a positive parabola, we will only have a minimum.

 

The vertex form is

 

y = a(x - h)²

 

 

where:

a is the coefficient of x² term

vertex is in the coordinate (h, k).  This will be the minimum.

 

y = 25(x² + (12/5)x + (36/25)) + 0

 

y = 25(x + 6/5)(x + 6/5) + 0

 

y = 25(x + (6/5))² + 0

 

 

h = -6/5

k = 0

 

The vertex is (-6/5 , 0).

 

The minimum is (-1.2 , 0).