Quadratic Functions definitions Flashcards
Quadratic Functions definitions
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Quadratic Function A polynomial of degree 2, typically written as f(x) = ax² + bx + c, whose graph forms a parabola. Parabola A symmetric, curved graph representing all quadratic functions, opening upward or downward. Standard Form An expression of a quadratic as f(x) = ax² + bx + c, where a, b, and c are real numbers and a ≠ 0. Vertex The point on a parabola representing either its maximum or minimum, given as an ordered pair. Axis of Symmetry A vertical line passing through the vertex, dividing the parabola into two mirror-image halves. X-Intercept A point where the parabola crosses the x-axis, found by solving f(x) = 0. Y-Intercept A point where the parabola crosses the y-axis, found by evaluating f(0). Vertex Form A quadratic written as f(x) = a(x-h)² + k, making transformations and the vertex easy to identify. Domain The set of all possible x-values for a quadratic, always all real numbers. Range The set of possible y-values for a quadratic, determined by the vertex and the direction the parabola opens. Vertical Stretch A transformation making the parabola narrower, occurring when |a| > 1 in the quadratic equation. Vertical Compression A transformation making the parabola wider, occurring when 0 < |a| < 1 in the quadratic equation. Horizontal Shift A movement of the parabola left or right, determined by the value of h in vertex form. Vertical Shift A movement of the parabola up or down, determined by the value of k in vertex form. Completing the Square A method for rewriting a quadratic from standard to vertex form by creating a perfect square trinomial.