Question

The maximum value of 5+20x-4x2, when x is a real number is

Answer 1

f(x) = 5 + 20x - 4x²
a = -4
b = 20
c = 5

y max 
= (b² - 4ac)/(-4a)
= [20² - 4 . (-4) . 5]/[-4 . (-4)]
= (400 + 80)/16
= 480/16
= 30

Answer 2

Solution :-

To find the value of x, coordinate we use :

x = - b/2*a  where, a = - 4 and b = 20

So, 

x = (- 20)/2*(- 4)

x = - 20/(- 8) 

x = 20/8

x = 5/2

Now, to find the value of y coordinate, we will substitute the x = 5/2 in the given equation.

⇒ - 4x² + 20 + 5

⇒ y = (- 4)*(5/2)² + 20*(5/2) + 5

⇒ (- 4)/(25/4) + 100/2 + 5

⇒ - 25 + 50 + 5

⇒ 55 - 25

⇒ y = 30

This is the value of y coordinate of the vertex (maximum).

Answer