Chapter 12: Quadratic expressions, equations and graphs

The chapter problem

The ball's path

A ball follows a path that can be modelled by a quadratic graph. Its height $h$ metres after $t$ seconds is $h=-t^2+4t+5$.

First contact: before calculating, predict when the ball reaches the ground. You can make a guess; you will return to this question after learning several methods.

By the end of this chapter you will be able to

• expand and factorise quadratic expressions;
• sketch and interpret quadratic graphs, including their roots and turning points;
• solve quadratic equations by factorising, using a formula, or completing the square;
• choose a method and explain why it fits the expression.

Roadmap

• 12.1 Expanding and factorising quadratics
• 12.2 Factorising harder quadratics
• 12.3 Quadratic graphs and their features
• 12.4 Solving quadratic equations by factorising
• 12.5 The quadratic formula
• 12.6 Completing the square
• Review

Make a connection

Where might you or someone you know need to find when a changing quantity reaches a particular value? Write one example in your own words.