Anatomy of a Parabola

Algebra 1 · Axiom Academy

Every parabola wears the same four landmarks — vertex, axis of symmetry, direction of opening, and intercepts. Learn to read them straight off the curve. A parabola is the smooth, symmetric U you get from a quadratic function. The simplest one is y = x^2 : it bottoms out at the origin and curves up the same way on both sides. Play the animation to watch the curve get drawn point-by-point. The general quadratic — every parabola has this form The vertex is the turning point — the lowest point if the parabola opens up, the highest if it opens down. Its x -coordinate is always ; plug that back in to get the y . Watch the dot slide down the curve and lock onto the bottom. Axis x-value, then evaluate for y Here a = 1 and b = -2 , so . Then y = (1)^2 - 2(1) - 3 = -4 . The axis of symmetry is the vertical line through the vertex that splits the parabola into two mirror-image halves. Its equation is — the same value as the vertex's x . The animation drops the axis, then shoots mirror-point pairs out to show both sides match. A vertical line — points the same distance left and right share a y-value For y = x^2 - 2x - 3 , the axis is x = 1 . Go the same distance left and right of the axis and the heights match: at x = 0 and x = 2 , both give y = -3 .

This is the written version of the interactive lesson above. See the full Algebra 1 course.