<span>y = 2.5x^2 - 13x + 12
The equation for a parabola is a quadratic equation of the form
y = ax^2 + bx + c
So let's calculate a, b, and c.
First thing to note is that we have the y-intercept, so x is 0. That means that we have
12 = a*0^2 + b*0 + c
12 = 0 + 0 + c
12 = c
So we now know c which is 12.
Now with the two intercepts we have
ax^2 + bx + 12 = 0 where x is 1.2 or 4. So let's set them equal to each other. Then solve for b in terms of 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
