<PRE><B>Question 384161</B>
finding the polynomial equation where f(0)=f(5)=0 and f(2)=-12.
:
Using the form y = ax^2 + bx + c; (a 2nd degree equation)
:
When the y intercept is 0, then c = 0, therefor the equation becomes just:
y = ax^2 + bx
:
f(5)=0 then x=5; y=0
5^2a + 5b = 0
25a + 5b = 0
:
f(2)=-12: x=2; y=-12
2^2a + 2b = -12
4a + 2b = -12
:
Use elimination, multiply the 1st equation by 2, the 2nd equation by 5:
50a + 10b = 0
20a + 10b = -60
-------------------subtraction eliminates b, find a
30a = +60
a = 2
:
Find b using the 1st equation:
25(2) + 5b = 0
50 + 5b = 0
5b = -50
b = -10
:
the equation: f(x) = 2x^2 - 10x</PRE>