Vertex and intercepts of a parabola

The graph of a quadratic function is a parabola. Its lowest or highest point is called the vertex. We find it by completing the square: x² − 6x + 5 = (x − 3)² − 4, so V = (3, −4). The vertical line through the vertex, here x = 3, is the axis of symmetry of the parabola.

What does this generator do?

At the easy level the formula has the form x² + bx + c and you find the vertex. At the medium level the number in front of x² is not 1 and you also find the y-intercept. At the hard level you find the vertex and the x-intercepts. Sometimes the graph does not cross the x-axis at all.

How to use it

1) If there is a number a in front of x², take it outside a bracket. 2) Complete the square: x² + bx = (x + b/2)² − (b/2)². 3) From the form a(x − m)² + n read the vertex V = (m, n). 4) You get the y-intercept by substituting x = 0. 5) The x-intercepts are the solutions of the equation f(x) = 0.