Quadratic Formula — Worked Examples
Five real-world examples demonstrating the Quadratic Formula formula ((-b±√Δ)/2a).
1
Two Real Roots
Classic case with two solutions
Inputs
a 1
b -3
c 2
Result
x 2.000, 1.000
2
One Root (Perfect Square)
Parabola just touches the axis
Inputs
a 1
b -4
c 4
Result
x 2.000, 2.000
3
No Real Roots
Parabola above x-axis entirely
Inputs
a 1
b 0
c 1
Result
x No real roots
4
Projectile Landing
Ball thrown at 20m/s from height 5m
Inputs
a -4.9
b 20
c 5
Result
x 4.318, -0.236
5
Profit Maximization
Finding breakeven points
Inputs
a -2
b 10
c -8
Result
x 4.000, 1.000