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.

    Lead into completing the square.
    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

  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

  14. Monday 23 August, period 1

    Starter from Beverley (above).

    Revision of graphs of Exponential and Logarithmic functions.

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