Find a quadratic function Fx that takes its largest value of

Find a quadratic function F(x) that takes its largest value of 400 at x = 5, and express is in standard form F(x) = ax^2 + bx + c. Give the values of a, b, an Assume the leading coefficient is plusminus 1. a = b = c =

Solution

F(x) = ax^2 +bx +c

Max at x= -b/2a = 5

b = -10a -----(1)

Now F(x) = 400 at x= 5

400 = 25a +5b +c -----(2)

Given leading coefficient a = +/-1

So, b = -10 ; b = 10

a=-1 ; b = 10 ; 400 = 25*(-1) +5*10 +c

c = 375

a=1 ;b = -10 ; 400 = 25 -50 +c

c = 425

So,    F(x) = -x^2 + 10x +375

or   F(x) = x^2 - 10x +425