Quadratic Graphs (Cambridge (CIE) IGCSE Maths: Extended)

 The diagram shows a sketch of the curve  .

Find the coordinates of the points A, B and C.

A (.............. , ..............)

B (.............. , ..............)

C (.............. , ..............)

i) Factorise  .   

[2]

ii) The diagram shows a sketch of  .

Work out the values of ,  and .

................................................     

  ................................................     

  ................................................ [3]

Write    in the form  

Sketch the graph of  ,  indicating the coordinates of the turning point.

On the diagram,

Sketch the graph of .

Find the turning point of    by completing the square.  

( ...................... , .....................)

The curve    is drawn on a grid.

A line is drawn on the same grid.

The points of intersection of the line and the curve are used to solve the equation 

Find the equation of the line in the form 

..................................................

The graph of  is shown on the grid.

By drawing a suitable line on the grid, solve the equation .  

.................... or ....................

Complete the table of values for 

On the grid, draw the graph of y = x² – 2x for values of x from –2 to 4

Solve 

The diagram shows the graph of

Use the graph to find estimates for the solutions of

i)    

ii)    

Use the graph to find estimates for the values of x that satisfy the simultaneous equations

The curve has equation    where 

Using the axes below, sketch the curve .
On your sketch show clearly, in terms of ,

i) the coordinates of any points of intersection of  with the coordinate axes,

ii) the coordinates of the turning point.

The curve  has equation 

Using the axes below, sketch the curve . On your sketch show clearly

i) the exact coordinates of any points of intersection of  with the coordinate axes,

ii) the coordinates of the turning point.