quadratic Functions and graphs

Graphs of Quadratic Function

A Quadratic Function is of the form y = ax² + bx + c (a, b and c are numbers and a ≠ 0).

If a>0, the graph is of U- shape and will have a minimum point.

If a<0, the graph is of inverted U - shape and will have a maximum point.

The graph will cross the y-axis at the point c and are symmetrical about vertical line that passes through maximum or minimum point.

y = (x – p)² + q , y = – (x – p)² + q

y = (x – p)² + q will have a minimum point at (p , q) and symmetrical about the line x = p.

y = – (x – p)² + q will have a maximum point at (p , q) and symmetrical about the line x = p.

y = (x – a)(x – b), y = – (x – a)(x – b)

y = (x – a)(x – b)will intersect the x axis at x=a, x=b and will have a minimum point.

y = – (x – a)(x – b) will intersect the x axis at x=a, x=b and will have a maximum point.

y = 1/x², y = –1/x²

y = x³, y = –x³