Quadratic Functions Flashcards

Grade 10 · Math · Flashcards

Key vocabulary and formulas for quadratic functions and parabolas.

Flashcards

Quadratic function: A function of the form f(x) = ax² + bx + c where a ≠ 0
Parabola: The U-shaped graph of a quadratic function
Vertex: The minimum or maximum point of a parabola; located at (h, k) in vertex form
Vertex form: f(x) = a(x - h)² + k; the vertex is (h, k)
Standard form: f(x) = ax² + bx + c
Axis of symmetry: The vertical line x = -b/(2a) that passes through the vertex
Discriminant: b² - 4ac; tells you how many real roots a quadratic has
Discriminant > 0: Two distinct real roots (two x-intercepts)
Discriminant = 0: One repeated real root (parabola tangent to x-axis)
Discriminant < 0: No real roots (parabola doesn't cross x-axis)
a > 0 in f(x) = ax² + bx + c: Parabola opens upward; vertex is a minimum
a < 0 in f(x) = ax² + bx + c: Parabola opens downward; vertex is a maximum
Y-intercept of a quadratic: Always equal to c in standard form ax² + bx + c; found by evaluating f(0)
Zeros / roots of a quadratic: The x-values where f(x) = 0; also called x-intercepts
Completing the square: Algebraic method to convert standard form to vertex form by creating a perfect square trinomial