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Quadratic Equations (Cambridge O Level Maths)

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Quadratic Equations

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Quadratic Equations

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1a
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Write x squared space space – space 4 x space plus space 7 space in the form open parentheses x minus a close parentheses squared space plus b.

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1b
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Write down the coordinates of the turning point of the graph of y space equals space x squared space – space 4 x space plus space 7 space.

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2
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Write  x squared plus 10 x plus 14  in the form  open parentheses x plus a close parentheses squared space plus b.

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3
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x squared plus 4 x minus 9 equals left parenthesis x plus a right parenthesis squared plus b

Find the value of a and the value of b.
 

  a = ............................................
b = ............................................

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1
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i)

Write x squared plus 8 x minus 9 space in the form space open parentheses x plus k close parentheses squared plus h.
 

[2]

ii)

Use your answer to part (i) to solve the equation space x squared plus 8 x minus 9 equals 0.
 

x equals................... or x equals................... [2]

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2
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Solve by factorisation 10 r squared minus 23 r plus 9 equals 0. 
  

r = ................... or r = ................... 

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3
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x squared minus 12 x plus a equals left parenthesis x plus b right parenthesis squared
 
Find the value of a and the value of b.
 

a = ...............................................
b = ...............................................

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4a
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Write x to the power of 2 space end exponent – space 6 x space – space 19 in the form left parenthesis x space – space a right parenthesis squared space plus space b space.

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4b
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Using your answer to part (a), write down the coordinates of the turning point of the graph of y space equals space x squared space – space 6 x space – space 19 .

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1
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The solutions of the equation space x squared plus b x plus c equals 0 space are fraction numerator negative 7 plus square root of 61 over denominator 2 end fraction and fraction numerator negative 7 minus square root of 61 over denominator 2 end fraction.
 
Find the value of b and the value of c.
 

b equals ................................................  
c equals ................................................  

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2
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cie-igcse-2019-may-jun-p4-tz1-q7b 
The difference between the areas of the two rectangles is 62 cm2.

i)
Show that x squared plus 2 x minus 63 equals 0.
 
[3]
ii)
Factorise x squared plus 2 x minus 63.
 
[2]
iii)
Solve the equation x squared plus 2 x minus 63 equals 0 to find the difference between the perimeters of the two rectangles.
 
.............................................. cm [2]

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3
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q6-veryhard-2-5-quadratic-equations-cie-igcse-maths-extended

The lengths of the sides are in centimetres.
The area of triangle T1 is equal to the area of triangle T2.
Work out the value of x, giving your answer in the form a plus square root of b where a and b are integers.

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