Complete analysis of y = ax² + bx + c
y = 1x² -4x +3
Parabola Direction
upward ∪
a = 1
Extreme Point
Minimum at (2, -1)
Vertex
Axis of Symmetry
x = 2
y-intercept
(0, 3)
Discriminant (Δ)
Δ = 4
Roots (x-intercepts)
x₁ = 1, x₂ = 3
Formula: x = (-b ± √Δ) / 2a
Domain
ℝ (all real numbers)
Range
[-1, ∞)
Decreasing on:
x < 2
Function decreases before vertex
Increasing on:
x > 2
Function increases after vertex
Positive (y > 0):
x < 1 or x > 3
Negative (y < 0):
1 < x < 3
