**New Topic:** Algebraic Functions and Graphs

By the end of this topic you will be able to:

• complete the square for quadratic functions

• recognise the probable form of a function from its graph

• draw graphs of related functions given *f(x)*, *f(x)* being a simple polynomial or trigonometric function

• know the general features of the graphs of *y=a ^{x}* and

*y=log*

_{a}x
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Filed under: Higher | Tagged: exponentials, functions, Higher, logs, quadratics |

Mr H, on Tuesday 22 June, 2010 at 21:03 said:Wednesday 23 June, periods 5 & 6Mental warm-up: squaring brackets, e.g. (x + 2)²

Practice factorising then look at quadratic function on graphics calculator.

Look at link between values in trinomial and factors with the graph.

Recap translating the y = x² function.

Lead into completing the square.

Finish lesson with a class created exercise completing the square. e.g. x² + 4x – 1

Mr H, on Wednesday 23 June, 2010 at 22:10 said:Quite a lot of ground covered today. A lot of work done on getting reaquainted with the quadratic function and its graph.

Time spent translating the graph – we will come back to this again later.

Basic completing the square practiced at the end of the lesson.

Mr H, on Wednesday 23 June, 2010 at 22:15 said:Thursday 24 June, period 2Starter from Amy (see Straight Line comments).

Use Show-me boards to practice translating functions.

e.g. move y = x² two units left and three down, etc.

Ask class to create trinomials to complete the square.

Aim to cover basic examples, odd x coefficients and max TP quadratics,

e.g. y = 1 + 2x – x²

Homework due today!Mr H, on Thursday 24 June, 2010 at 13:18 said:Spent longer on starter and recap than planned to ensure everyone secure.

Covered basic examples and odd x coefficients.

Mr H, on Thursday 24 June, 2010 at 21:59 said:Friday 25 June, period 5We need to get stuck straight into the algebra today and cover a good bit of ground.

Quick practice of completing the square skills to date then onto quadratics with squared coefficient >1, then negative.

Homework due Thursday 1 July:More details on the homework page on school website: Euler Line Investigation

cameron, on Saturday 26 June, 2010 at 20:15 said:this is too confusing!

Mr H, on Sunday 27 June, 2010 at 11:12 said:What have you found out so far?

Where have you looked for information?

Mr H, on Friday 25 June, 2010 at 15:41 said:Fire alarm practice!!

Managed to look at more complicated trinomials but no max TP examples.

Mr H, on Sunday 27 June, 2010 at 23:30 said:Monday 28 June, period 1Starter question to lead into key points from HW:

Find the equation of the straight line which passes through the point (3,-1) and is:

(a) parallel to the line with equation x = -1

(b) perpendicular to the line with equation 3y – 2x = 5

(c) parallel to the line with equation y + ½x = 4

Feedback on straight lines homework.

Completing the Square – further practice including a negative x² terms.

Ensure class have enough worked examples to work independently next lesson as I will not be in class on Tuesday.

Mr H, on Monday 28 June, 2010 at 23:19 said:All above covered

Mr H, on Monday 28 June, 2010 at 23:20 said:Tuesday 29 June, period 4I will be unavailable this period so class left to work through a Completing the Square worksheet.

Mr H, on Wednesday 30 June, 2010 at 0:09 said:Wednesday 30 June, periods 5 & 6Starter: What is the maximim value of 1/(x² – 4x + 7)?

Check completing the square exercise completed yesterday and deal with any issues.

Check progress with Euler line task.

Recap of translating y = x²

Look at other familiar functions, e.g. y = x³, straight lines and trig functions.

Then investigate the exponential function (and logarithmic if time).

Reminder: Euler Line investigation report due tomorrow

Mr H, on Thursday 1 July, 2010 at 0:07 said:Almost all of above completed although more time required on exponential and log function not reached.

Mr H, on Thursday 1 July, 2010 at 0:08 said:Thursday 1 July, period 2Euler Line investigations due today.

Discuss results and hear contributions from each group on how they solved the problem and what they found out along the way.

Peter

willhave a starter problem prepared for the lesson!Beverley Breese, on Sunday 22 August, 2010 at 22:00 said:Complete the square:

y = x² + 7x – 3

y = 3x² – 9x + 4

Mr H, on Sunday 22 August, 2010 at 22:04 said:Thanks Beverley!

I like how you chose ones with fractions!! 😉

Mr H, on Sunday 22 August, 2010 at 22:04 said:Monday 23 August, period 1Starter from Beverley (above).

Revision of graphs of Exponential and Logarithmic functions.