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Quadratic Formula

Algebra HOME | Achievement Objectives | Simplify | Expanding | Factorising | Indices | Rearrange | Logs | Fractions | Linear Equations | Inequations | Solving Quadratics equations | Quadratic Formula | Revision

19

Quadratic Formula

Using the Quadratic formula to solve a quadratic.
Practice of quadratic applications involving the quadratic formula.

Activity
Quadratic formula to solve | Mixed problems (www.transum.org)

Class notes, Blank notes

Ex6.06, Ex 6.05

Illuminations completing the square

Theta pg 24

NuLake EAS Q398 - 419

GeoGebra Java G

20

Quadratic Applications

Forming a quadratic equation from an applivation problem.
Solving quadratic problems in context.

 

Class notes, Blank notes

Ex6.07, Ex 6.08

Theta pg 25

NuLake EAS Q393 - 397 & 418, 419

21 Nature of roots

Establishing the nature of roots & using the discriminant to determine if there are none, one or two solutions (roots) to a quadratic problem

 

Class notes, Blank notes

Ex6.09, Ex6.10

Theta pg 26

NuLake EAS Q420 - 440

23



Graph intersections

Finding the points of intersection between lines & parabolas, circles, hyperbola.
Solving simultaneous equations involving substitution and solving a quadratic by factorising, completing the square, or the quadratic formula.
Applications of intersections and problems in context

 

Class notes, Blank notes

Ex7.01, Ex7.02, Ex7.03

points of intersection

Theta pg 27 & 28

NuLake EAS Q441- 445





Intersections

Determining the points of intersection between functions: line & parabola,  line & circle, line & hyperbola, Tangency

Blank notes | Absolute value graphs bland notes

 

 

Khan Academy Solving Quadratics

 

 

 

To solve a quadratic equation the factorising can be very difficult.
The quadratic formula finds the solutions avoiding the factorising process.
Be careful with negatives.

Investigating the quadratic formula and the quadratic graph roots (Thanks to Sue Berg)

The quadratic formula

An example

Working

Solution

2nd example

Working

Solution

Mouse over key words

 

 

Summary:

example 1 example 2

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The Descriminant

The part of the quadratic formula in the square root is the descriminant.
This tells us if there is one, two or no (real) solutions

The quadratic formula

The descriminant

Two solution

One solutions

No (real) solutions

Mouse over key words

 

Summary:

 

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