This unit is part of the special topic “Bringing the Real World into Algebra”. Students match quadratic graphs to paths such as water spouting from a hose, and the flight of a football. These lessons reveal the links between the graphs of quadratic functions and the three algebraic forms (turning point form, product, sum of three terms) and the influence of the parameters in the functions.

### Lesson 1: Fitting Curves

Students are introduced to GeoGebra (or alternative software), by fitting lines to a digital image. This is extended to curve fitting using the turning point form for quadratic functions. Students make systematic adjustments to the function rule to fit the curve to an image of water from a hose or the path of a ball.

### Lesson 2: Trajectories

Students take a set (burst) of photos of the path of a ball, and fit a parabola to points from the images by systematically altering the parameters of the quadratic function. The usefulness of the turning point form (highest point reached) and of the factorised form (distance travelled) are explored in this context.

### Lesson 3: Linking Different Forms

Students compare different symbolic forms for the same quadratic function using GeoGebra, and then by hand sketching. Further practice using text book type examples is suggested for fluency.

Last updated December 11 2018.