Δ = b²-4ac: positive → 2 real roots, zero → 1 root (double root), negative → no real roots (complex roots).

Here a=1, b=-3, c=2. Δ = 9-8 = 1. x = (3 ± 1) / 2. x₁ = 2, x₂ = 1.

The vertex is the highest or lowest point of the parabola. x-coordinate: -b/(2a), y-coordinate is found by substituting x into the equation.

Question 1

What is the quadratic formula?

Accepted Answer

x = (-b ± √(b²-4ac)) / 2a. The discriminant Δ = b²-4ac tells the number of real roots: Δ>0 two roots, Δ=0 one root, Δ<0 complex roots.

Question 2

What does the discriminant tell us?

Accepted Answer

Δ = b²-4ac: positive → 2 real roots, zero → 1 root (double root), negative → no real roots (complex roots).

Question 3

How do I solve x²-3x+2=0?

Accepted Answer

Here a=1, b=-3, c=2. Δ = 9-8 = 1. x = (3 ± 1) / 2. x₁ = 2, x₂ = 1.

Question 4

What is the vertex?

Accepted Answer

The vertex is the highest or lowest point of the parabola. x-coordinate: -b/(2a), y-coordinate is found by substituting x into the equation.

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