Quadratic function and graphs

Content

  • Quadratic Equations

  • Graph of Quadratic Function when a>0

  • Graph of Quadratic Function when a>0


Quadratic Equations

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

Graph of Quadratic Function when a>0


If a>0, the graph is of U shape.

The graph will have a minimum point

The line of symmetry will pass through the minimum point.

The graph will cross the y-axis at the point c.

Graph of Quadratic Function When a<0


If a<0, the graph is of inverted – U shape.

The graph will have a maximum point.

The line of symmetry will pass through the maximum point.

The graph will cross the y-axis at the point c.

Quadratic Curve - Interactive

Questions

  1. There are x people in the room. Each person in a room shakes hand with every other person in the room exactly once. The total number of handshakes is 90. Form a quadratic equation in x and solve it to find the number of people in the room.

  2. The cost of a present is $200 and to be shared equally among a group of x friends. When two more friends joined the group, every one paid $5 less. Form a quadratic equation in x and solve it to find the number of friends in the group now.