VertexThe turning point, where the parabola meets its axis of symmetry. This one opens up, so the vertex is its minimum: (1, −4).
Axis of symmetryThe line that splits the parabola into mirror halves. It runs through the vertex and the focus: here x = 1.
FocusThe fixed point inside the curve. Every point on the parabola is the same distance from the focus as from the directrix: here (1, −3).
DirectrixThe fixed line outside the curve. It is on the far side of the vertex from the focus: here y = −5.
x-interceptsThe points where the parabola crosses the x-axis. Also called the zeros or roots: (−3, 0) and (5, 0).
y-interceptThe point where the parabola crosses the y-axis: here (0, −3.75).
How this list was compiled: Read 2026-09-26. OpenStax College Algebra 2e, section 5.1 Quadratic Functions, https://openstax.org/books/college-algebra-2e/pages/5-1-quadratic-functions : the parabola as the U-shaped graph of a quadratic function; the vertex as its extreme point, the minimum when it opens up; the axis of symmetry as the vertical line through the vertex; the y-intercept where it crosses the y-axis; the x-intercepts where it crosses the x-axis, the zeros or roots. Wikipedia, Parabola, https://en.wikipedia.org/wiki/Parabola : the focus and directrix, every point of the parabola equidistant from both; the axis of symmetry through the focus perpendicular to the directrix; the vertex where the parabola meets its axis. The drawn curve is y = (x − 1)²/4 − 4, so p = 1: vertex (1, −4), focus (1, −3), directrix y = −5, x-intercepts −3 and 5, y-intercept −3.75, checked by substitution. Licence: own work
The drawing: Drawn for this site by script, 2026-09-26. Own work. Licence: own work
How it works
The parts of a parabola on one graph, y = (x − 1)²/4 − 4: the vertex and axis of symmetry, the focus and directrix, and where the curve crosses each axis. The dashed lines show why the focus matters.
Read the full guide
Vertex and axis
The vertex is the turning point, here the lowest point, (1, −4). The axis of symmetry is the line through it that splits the curve into mirror halves, x = 1.
Focus and directrix
Every point on a parabola is as far from the focus as from the directrix. From (5, 0) the dashed lines show it: 5 to the focus at (1, −3), and 5 down to the directrix, y = −5.
The focus is always inside the curve and the directrix outside it, the same distance from the vertex.
Questions and answers
What is the vertex of a parabola?
The turning point where the parabola meets its axis of symmetry. If the parabola opens up it is the lowest point, the minimum; if it opens down it is the highest point, the maximum.
What are the x-intercepts of a parabola called?
They are also called the zeros or roots: the x-values where y = 0. A parabola can have two, one or none.
What is the directrix of a parabola?
A fixed line outside the curve. Every point on the parabola is the same distance from the directrix as from the focus.