Hello, maxboy0801!
The answer is indeed a = 2 . . . How did you get that?
A certain parabola, \(\displaystyle y\,=\,ax^2\,+\,bx\,+\,c\), passes through the three points (1, 9), (-1, 3), and (-2, 6).
If so, then a = __
You are given three point
on the parabola.
For example, (1, 9) tells us: when x = 1, y = 9.
Plug those values into the equation:
.\(\displaystyle 9\:=\:a\cdot1^2\,_+\,b\cdot1\,+\,c\;\;\Rightarrow\;\;a\,+\,b\,+\,c\:=\:9\)
.[1]
(-1,3) gives us:
.\(\displaystyle 3\:=\:a(-1)^2\,+\,b(-1)\,+\,c\;\;\Rightarrow\;\;a\,-\,b\,+\,c\:=\:3\)
.[2]
(-2,6) gives us:
.\(\displaystyle 6\:=\:a(-2)^2\,+\,b(-2)\,+\,c\;\;\Rightarrow\;\;4a\,-\,2b\,+\,c\:=\:6\)
.[3]
Solve the system of equations . . .
. . . I got: \(\displaystyle a=2,\,b=3,\,c=4]\)
