Quadratic Graphs (Cambridge International IGCSE Mathematics): Exam Questions

Write $x^{2}+10x+14$ in the form $( x + a )^{2} + b.$

Extract:

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

Sketch the graph of $y=x^{2}+10x+14$, indicating the coordinates of the turning point.

Find the turning point of $y=x^{2}+4x-3$ by completing the square.

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

The diagram shows a sketch of the curve $y=x^{2}+3x-4$.

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

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

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

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

i) Factorise $24+5x-x^{2}$.

ii) The diagram shows a sketch of $y=24+5x-x^{2}$.

Work out the values of $a$, $b$ and $c$.

$a=$ ................................................

$b=$ ................................................

$c=$................................................ [3]

On the diagram,

Sketch the graph of $y = ( x - 1 )^{2}$.

(i) Write $6x-0.5x^{2}-7$ in the form $y = a ( x - p )^{2} + q$

(ii) Hence, write down the coordinates of the turning point on the curve with equation $y=6x-0.5x^{2}-7$

State the nature of this turning point.

State the equation of the axis of symmetry.

The curve $C$has equation $y=4(x-1)^{2}-a$ where $a>4$

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

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

ii) the coordinates of the turning point.

The curve $C$ has equation $y=x^{2}--6x+4$

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

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

ii) the coordinates of the turning point.