Answer: x^2 - 3x + 2
Step-by-step explanation:
formula for quadratic equation
y = ax^2 + bx + c
to solve this, we need at least three points
use (1, 0), (0, 2), and (-1, 6)
since the y-intercept is at (0,2), c = 2
plug in values for (1,0), x= 1, y = 0, c = 2
y = ax^2 + bx + c
0 = a(1^2) + b(1) + 2
0 = a + b + 2
write a in terms of b
a = - b - 2
plug in values for (-1, 6), x = -1, y = 6, c = 2
6 = a(-1^2) + b(-1) + 2
6 = a - b + 2
4 = a - b
so we have two equations, plug a into the second equation
a = - b - 2
4 = a - b
4 = (-b - 2) - b = -2b - 2
b = -3
plug b back into a = - b - 1
a = -(-3) - 2 = 1
plug a, b, and c back into y = ax^2 + bx + c
so your equation is x^2 - 3x + 2
