Quadratic Functions & Graphs (DP IB Applications & Interpretation (AI)): Revision Note

Quadratic Functions & Graphs

What are the key features of quadratic graphs?

• A quadratic graph is of the form where .

• The value of a affects the shape of the curve

  • If a is positive the shape is 

  • If a is negative the shape is 

• The y-intercept is at the point (0, c)

• The zeros or roots are the solutions to 

  • These can be found using your GDC or the quadratic formula

  • These are also called the x-intercepts

  • There can be 0, 1 or 2 x-intercepts

• There is an axis of symmetry at 

  • This is given in your formula booklet

  • If there are two x-intercepts then the axis of symmetry goes through the midpoint of them

• The vertex lies on the axis of symmetry

  • The x-coordinate is 

  • The y-coordinate can be found using the GDC or by calculating y when 

  • If a is positive then the vertex is the minimum point

  • If a is negative then the vertex is the maximum point