Question 1

How does the Discriminant (Δ = b² - 4ac) predict roots?

Accepted Answer

If Δ > 0, the equation has two distinct real roots. If Δ = 0, it has exactly one repeated real root (tangent to x-axis). If Δ < 0, it has two complex conjugate roots (no real x-intercepts).

Question 2

How is the parabola vertex (h, k) calculated?

Accepted Answer

The x-coordinate of the vertex (and axis of symmetry) is h = -b / (2a). Evaluating the quadratic at h gives the extremum value k = f(h).

Question 3

What is vertex form vs standard form?

Accepted Answer

Standard form is ax² + bx + c = 0. Vertex form is a(x - h)² + k = 0, directly revealing the parabola maximum/minimum turning point.

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