Mastering Quadratic Equations

• Nieuwe lesbewerker

Mastering Quadratic Equations

What do you already know about solving quadratic equations?

Learning Objective

At the end of the lesson you will be able to solve quadratic equations using different methods, explain each method, and confidently tackle related problems.

What is a Quadratic Equation?

A quadratic equation is any equation of the form axb + bx + c = 0, where a  0. The graph of a quadratic is a parabola.

Methods for Solving Quadratics

1. Factorising 2. Using the quadratic formula 3. Completing the square We'll see examples of each.

Example 1: Solve by Factorising

Solution

x5 - 6x + 5 = (x - 5)(x - 1) = 0 So x = 5 or x = 1

Solve x5 - 6x + 5 = 0 by factorising.

Question

Example 2: Quadratic Formula

x = [-3 b c(9 + 16)]/2 = [-3 b 5]/2 So x = 1 or x = -4

Solve x2 + 3x - 4 = 0 using the quadratic formula.

Question

Solution

Practice Time

1. Solve x5 - 9x + 14 = 0 by factorising. 2. Use the formula to solve x2 + 2x - 8 = 0. 3. Try completing the square to solve x2 + 6x + 5 = 0.

Summary and Reflection

You have learnt multiple methods for solving quadratic equations. Which method do you find easiest and why?

Write down 3 things you learned in this lesson.

Write down 2 things you want to know more about.

Ask 1 question about something you haven't quite understood yet.