Flashcards: Quadratic Roots and Discriminant Mastery — 18 cartões

Roots of quadratic — definition?

Values of x where f(x)=0.

Roots as f(x)=0 — role?

Identify x-intercepts of parabola.

Factored form — purpose?

Express quadratic using roots explicitly.

Coefficient a — how found?

Substitute known point into factored form.

Discriminant D — formula?

D = b² - 4ac.

D > 0 — roots?

Two distinct real roots.

D = 0 — roots?

One repeated real root.

D < 0 — roots?

Complex conjugate roots.

Quadratic formula — purpose?

Find solutions using D and coefficients.

Standard to vertex form — method?

Complete the square.

Vertex form — structure?

f(x) = a(x - h)^2 + k.

Vertex — coordinates?

(h, k) from vertex form.

Max/min — where?

At the vertex (h, k).

X-coordinate of vertex?

x = -b / (2a).

Inverse function — process?

Swap x and y, solve for y.

Inverse of quadratic — form?

h ± √[(x - k)/a].

Square root — simplification?

Factor out perfect squares.

Combine radicals — when?

Like radicals with same radicand.