jika suatu fungsi kuadrat f(x) diketahui bahwa f(1)= f(3)=0 dan mempunyai nilai maksimum 1. tentukan f(x)!

f(1) = f(3)= 0

f(1) = 0 → (x,y) = (1,0)
f(3) = 0 → (x,y) = (3,0)

f(x) = a(x -1)(x - 3)
nilai maksimum = 1 → f(x)= 1
x= -1/2 (x1+x2) = -(3+1)/2 = -2
f(-2) = 1 → a(-2-1)(-2-3) = 1
a(-3)(-5) = 1
a= 1/15
f(x) = 1/15 (x - 1)(x - 3)
f(x)= 1/15 (x² - 4x + 3)