IGCSEMaths A: HigherEdexcelFlashcards

Completing the Square (Edexcel IGCSE Maths A)

Flashcards

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  • FrontCompleting the Square

    True or False?

    Completing the square involves writing a quadratic expression in terms of a squared bracket.

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Cards in this collection (7)

  • True or False?

    Completing the square involves writing a quadratic expression in terms of a squared bracket.

    True.

    Completing the square involves writing a quadratic expression in terms of a squared bracket.

    It takes the expression x squared plus b x plus c and writes it as open parentheses x plus p close parentheses squared plus q, where the first term is a squared bracket.

  • If an equation is given in completed-square form, such as open parentheses x plus 3 close parentheses squared minus 4 equals 0, explain how to solve it.

    If an equation is given in completed-square form, such as open parentheses x plus 3 close parentheses squared minus 4 equals 0, to solve it you need to make x the subject.

    Add 4 to both sides: open parentheses x plus 3 close parentheses squared equals 4

    Take plus-or-minus square roots: x plus 3 equals plus-or-minus 2

    Make x the subject: x equals plus-or-minus 2 minus 3 giving x equals negative 1 or x equals negative 5

    (Note that to solve it, you do not expand the brackets back out!)

  • To complete the square of x squared plus b x plus c , explain how to find the value of p in the expression open parentheses x plus p close parentheses squared plus q.

    Completing the square of x squared plus b x plus c gives the form open parentheses x plus p close parentheses squared plus q. The value of p is half of the value of b.

  • True or False?

    The coordinates of the turning point (vertex) of the quadratic curve y equals open parentheses x plus 3 close parentheses squared plus 5 are open parentheses 3 comma space 5 close parentheses.

    False.

    The coordinates of the turning point (vertex) of the quadratic curve y equals open parentheses x plus 3 close parentheses squared plus 5 are not open parentheses 3 comma space 5 close parentheses.

    The correct coordinates are open parentheses negative 3 comma space 5 close parentheses.

    This is a common mistake in the exam! If y equals open parentheses x plus p close parentheses squared plus q is the curve, then open parentheses negative p comma space q close parentheses are the coordinates of the turning point.

  • What is the first step to completing the square of the quadratic expression a x squared plus b x plus c where a is not equal to 1?

    The first step to completing the square of the quadratic expression a x squared plus b x plus c where a is not equal to 1 is to factorise out a.

    This gives a open square brackets x squared plus b over a x plus c over a close square brackets.

    You can then complete the square inside the big brackets.

    It helps to use big brackets here, to avoid confusing them with the smaller brackets when completing the square inside.

    Note that you cannot divide by a to get rid of it, as you are only given an expression in the question (not an equation).

  • True or False?

    The coordinates of the turning points on the curves y equals open parentheses x plus 2 close parentheses squared plus 4 and y equals 3 open parentheses x plus 2 close parentheses squared plus 4 are the same.

    True.

    The coordinates of the turning points on the curves y equals open parentheses x plus 2 close parentheses squared plus 4 and y equals 3 open parentheses x plus 2 close parentheses squared plus 4 are the same.

    The coordinates of the turning point on y equals a open parentheses x plus p close parentheses squared plus q are always open parentheses negative p comma space q close parentheses, regardless of the value of a (even if a less than 0).

  • Explain how writing x squared minus 4 x plus 9 in the form open parentheses x minus 2 close parentheses squared plus 5 shows that any output of the function straight f open parentheses x close parentheses equals x squared minus 4 x plus 9 is always greater than, or equal to, 5.

    If x squared minus 4 x plus 9 can be written as open parentheses x minus 2 close parentheses squared plus 5 by completing the square, then straight f open parentheses x close parentheses equals x squared minus 4 x plus 9 can be written as straight f open parentheses x close parentheses equals open parentheses x minus 2 close parentheses squared plus 5.

    Anything squared is either equal to zero or greater than zero. That means open parentheses x minus 2 close parentheses squared greater or equal than 0.

    Adding 5 to both sides gives open parentheses x minus 2 close parentheses squared plus 5 greater or equal than 5.

    The left-hand side is straight f open parentheses x close parentheses, so the line above can be written as straight f open parentheses x close parentheses greater or equal than 5.

    This shows that straight f open parentheses x close parentheses will always be greater than or equal to 5.

    (You can try it yourself: substitute in any input and the output will always be greater or equal than 5!)

1. Numbers & the Number System
2. Equations, Formulae & Identities
3. Sequences, Functions & Graphs
4. Geometry & Trigonometry
5. Vectors & Transformation Geometry
6. Statistics & Probability