SOLUTION: Given (-1,-2) (1,-4) (2,4) find the equation of the quadratic equation. f(x)=ax^2+bx+c -2=a(-1)^2+b(-1)+c -4=a(1)^2+b(1)+c 4=a(2)^2+b(2)+c -2=a-b+c -4=a+b+c 4=4a+2b+c ?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Given (-1,-2) (1,-4) (2,4) find the equation of the quadratic equation. f(x)=ax^2+bx+c -2=a(-1)^2+b(-1)+c -4=a(1)^2+b(1)+c 4=a(2)^2+b(2)+c -2=a-b+c -4=a+b+c 4=4a+2b+c ?      Log On


   

Question 1009091: Given (-1,-2) (1,-4) (2,4) find the equation of the quadratic equation.
f(x)=ax^2+bx+c
-2=a(-1)^2+b(-1)+c
-4=a(1)^2+b(1)+c
4=a(2)^2+b(2)+c
-2=a-b+c
-4=a+b+c
4=4a+2b+c
???????
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You made the correct system of equations, system%28a-b%2Bc=-2%2Ca%2Bb%2Bc=-4%2C4a%2B2b%2Bc=4%29.

Next, choose either row-reduction matrix operations; or elimination method, or substitution method.

Substitution method is the least advanced way, and as a start, take E1, solve for c:
a-b%2Bc=-2
c=-a%2Bb-2
c=b-a-2
and substitute into E2 and E3:
system%28a%2Bb%2Bb-a-2=-4%2C4a%2B2b%2Bb-a-2=4%29
-
system%282b-2=-4%2C3a%2B3b-2=4%29
-
system%282b=-2%2C3a%2B3b=6%29
-
system%28b=-1%2Ca%2Bb=2%29, which shows one of the coefficients, easily allowing for finding another by using that other's now known value...
a=2-b
a=2-%28-1%29
a=2%2B1
highlight%28a=3%29, and obviously just found as well, highlight%28b=-1%29.

You still want to find the value for c. Use any equation of the system that you want.