## Algebraic Functions and Graphs 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=ax and y=logax

### 17 Responses

1. Wednesday 23 June, periods 5 & 6

Mental 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.

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

2. 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.

3. Thursday 24 June, period 2

Starter 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!

4. Spent longer on starter and recap than planned to ensure everyone secure.
Covered basic examples and odd x coefficients.

5. Friday 25 June, period 5

We 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:

Find the equation of the Euler line of the triangle with
vertices A(-2, -4), B(2, 4) and C(12, -4).

More details on the homework page on school website: Euler Line Investigation

• this is too confusing!

• What have you found out so far?
Where have you looked for information?

6. Fire alarm practice!!

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

7. Monday 28 June, period 1

Starter 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.

8. All above covered

9. Tuesday 29 June, period 4

I will be unavailable this period so class left to work through a Completing the Square worksheet.

10. Wednesday 30 June, periods 5 & 6

Starter: 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

11. Almost all of above completed although more time required on exponential and log function not reached.

12. Thursday 1 July, period 2

Euler 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 will have a starter problem prepared for the lesson!

13. Complete the square:
y = x² + 7x – 3
y = 3x² – 9x + 4

• Thanks Beverley!

I like how you chose ones with fractions!! 😉

14. Monday 23 August, period 1

Starter from Beverley (above).

Revision of graphs of Exponential and Logarithmic functions.