y =
x2
+
x
+
Vertex—
Axis of symmetry—
Focus—
Directrix—
x-intercepts—
y-intercept—
Step by step
Analyse a parabola y = ax² + bx + c — vertex, axis of symmetry, focus, directrix and intercepts — with everything marked on a graph.
Step by step
Enter the coefficients a, b and c to get the vertex, focus, directrix and intercepts.
Type the coefficients of y = ax² + bx + c. a must not be zero for the graph to be a parabola.
The vertex is at x = −b ⁄ (2a); the axis of symmetry passes through it. The focus sits 1 ⁄ (4a) above the vertex and the directrix the same distance below.
The x-intercepts are the real roots of the quadratic (there may be two, one or none), and the y-intercept is (0, c).