Algebra 2 Conic Sections Flashcards

Study Notes

Lines

Horizontal lines represented by the equation y = 0; in standard form, it appears as y - k/b = 0, indicating a constant y-value at k.
Vertical lines defined by the equation x = 0; in standard form, written as x - h/a = 0, indicating a constant x-value at h.
Oblique lines described by the equation y = x; in standard form, expressed as y - k/b = x - h/a, showing the relationship between y and x with variable slopes.

Vees

Vertical vees characterized by the equation y = |x|; standard form represented as y - k/b = |x - h/a|, defining a V-shape opening upwards.
Horizontal vees based on the equation x = |y|; standard form is x - h/a = |y - k/b|, creating a V-shape opening towards the sides.

Staircases

Vertical staircases represented by the equation y = [[x]]; standard form is y - k/b = [[x - h/a]], illustrating a step function that increases vertically.
Horizontal staircases depicted by the equation x = [[y]]; standard form expressed as x - h/a = [[y - k/b]], representing a step function that increases horizontally.

Parabolas

Vertical parabolas characterized by the equation y = x^2; standard form written as y - k/b = (x - h/a)^2, where a and b represent scaling factors and are not unique.
Horizontal parabolas defined by the equation x = y^2; a and b are scaling factors that influence the shape and width of the parabola but are not unique.

Circles and Ellipses

Equations for circles include x^2 + y^2 = 1; in the general form, if a = b = r, it becomes (x - h)^2 + (y - k)^2 = r^2, indicating a circle centered at (h, k) with radius r.

Hyperbolas

Horizontal hyperbolas represented by the equation x^2 - y^2 = 1; this equation forms two branches that open left and right.
Vertical hyperbolas characterized by the equation y^2 - x^2 = 1; similar to horizontal hyperbolas but with branches opening upwards and downwards.
Rectangular hyperbolas defined by xy = 1; key features include not having unique scaling factors a and b while maintaining symmetry around the axes.

Description

Test your knowledge of conic sections with these flashcards focused on horizontal, vertical, oblique lines, and vees. Each card presents a term alongside its mathematical definition for easy study. Ideal for Algebra 2 students looking to reinforce their understanding of these concepts.