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