What does the discriminant tell you?

Positive means two real roots, zero means one, negative means no real roots.

No, if a=0 it becomes a linear equation, not quadratic.

What are other methods to solve quadratics?

You can also use factoring or completing the square.

The quadratic formula solves any equation of the form ax^2 + bx + c = 0. It always works, even when factoring is difficult or impossible.

x = (-b +/- sqrt(b^2 - 4ac)) / 2a

Where:

aCoefficient a — Coefficient of x squared term

bCoefficient b — Coefficient of x term

cConstant c — The constant term in the equation

xSolution — The values of x that satisfy ax^2+bx+c=0

Here's how to calculate quadratic equations step by step:

1Identify a, b, c: Write the equation in standard form ax^2 + bx + c = 0.
2Calculate discriminant: Compute b^2 - 4ac to determine the number of solutions.
3Apply the formula: Plug a, b, c into the quadratic formula to find x.
4Simplify: Reduce fractions and simplify radicals in your answer.

Following these 4 steps gives you the final quadratic equations value.

A ball thrown upward at 20 m/s from 1.5m height follows h = -4.9t^2 + 20t + 1.5; the quadratic formula finds when it hits the ground.

Quadratic equations model projectile motion, profit optimization, area problems, and many physics scenarios.

Always compute both the plus and minus roots.

The formula starts with -b, not b.

A negative discriminant means no real solutions exist.