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This Week's Investigations:
This Week's Investigations:
Last week we looked at factorising Quadratics; this week we start building on factorising by:
In part 1 - looking at what would factorise
In part 2 - I would like to remind you how to complete the square and assemble a proof for the "Quadratic Formula".
In part 3 - you will think about the different representations of Quadratics and what they tell you about the graphs.
Part 1
Part 1
Have a look through the questions below. They do increase in difficulty. Below the questions you should find a link to the solutions.
Factorising Quadratics problem.pdfPart 2 - Completing the Square
Part 2 - Completing the Square
Please watch the video below for a quick refresher of how to Complete the Square. Attempt the questions and then try to prove the Quadratic Formula.
x^2-4x-5
8x^2-9x+7
3-6x-x^2
The Vertex
The Vertex
Something to contemplate
Something to contemplate
How can completing the square help with finding the vertex/line of symmetry in a quadratic graph?
Now complete the square to solve the general quadratic ax^2+bx+c=0
The result should look familiar.
You can use the card sort below to help you!
A Maximisation Problem
A Maximisation Problem
Can you solve this problem about maximising an enclosure size?
We need to solve maximisation and minimisation problems all the time - from maximising profits to making airplanes fly.
Part 3 - Equations and Graphs
Part 3 - Equations and Graphs
What can you tell about the graph from the equation and vice-versa . You may find this graphing website useful:
Quadratics are useful?
Quadratics are useful?
Why care about quadratic graphs at all? Well, if you want your maths to be in some way useful then have a look at this article explaining about parabolic mirrors - this is all based on results you can prove with A-Level Maths.
This Week's Tests and Last Week's Solutions
This Week's Tests and Last Week's Solutions
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