Answer:
y = [tex]x^{2}[/tex] - 2x - 3
Step-by-step explanation:
We know: y=ax^2+bx+c
Given: (2, 5), (3, 12), and (-1, -4)
so...
We plug in these numbers:
5 = a*(2^2) + b*2 + c
12 = a*(3^2) + b*3 + c
-4 = a*((-1)^2) + b*(-1) + c
simplify:
5 = 4a + 2b + c
12 = 9a + 3b + c
-4 = a - b + c
Solve this 3 variable system
Combine 5 = 4a + 2b + c and -4 = a - b + c
-8 = 2a - 2b + 2c from multiplying the equation -4 = a - b + c by 2
5 - 8 = 4a + 2a + 2b - 2b + c + 2c
-3 = 6a + 3c
-1 = 2a + c
next multiply -4 = a - b + c by 3
-12 = 3a - 3b + 3c add to 12 = 9a + 3b + c
-12 + 12 = 3a + 9a + -3b + 3b + 3c + c
0 = 12a + 4c
0 = 3a + c
combine -1 = 2a + c and 0 = 3a + c
1 = -2a - c
0 + 1 = 3a - 2a + c - c
1 = a
so... -1 = 2*1 + c
-1 = 2 + c
c = -1 -2 = -3
use equation -4 = a - b + c , solve for b
-4 = 1 - b + (-3)
-4 = -2 - b
b = -2 + 4 = -2
so a = 1, b = -2, c = -3
y = x^2 - 2x - 3
y = [tex]x^{2}[/tex] - 2x - 3
