Write the equation for the parabola that has x− intercepts (1.2,0) and (4,0) and y− intercept (0,12).

Equation of a parabola is written in the form of f(x)=ax²+bx+c.
The equation passes through points (4,0), (1.2,0) and (0,12), therefore; 
 replacing the points in the equation y = ax² +bx+c 
we get  0 = a(4)²+b(4) +c   for (4,0)
             0 = a (1.2)²+ b(1.2) +c for (1.2,0)
             12 = a(0)² +b(0) +c   for (0,12)
simplifying the equations we get
16a + 4b + c = 0
1.44a +1.2b + c = 0
+c = 12
thus the first two equations will be
16a + 4b = -12
1.44 a + 1.2b = -12 solving simultaneously 
the value of a = 5/2 and b =-13
Thus, the equation of the parabola will be given by;
 y= 5/2x² - 13x + 12 or y = 2.5x² - 13x + 12