WJEC GCSE Maths
Topic questions Pure mathematics Quadratic graphs
26 questions · 121 marks · about 2.5 hours
The table below shows some of the values of y = 2x2 − 6 for values of x from –3 to 2.
| x | – 3 | – 2 | – 1 | 0 | 1 | 2 |
| y = 2x2 − 6 | 2 | – 4 | – 6 | 2 |
Complete the table above.
On the graph paper opposite, draw the graph of y = 2x2 − 6 for values of x
from –3 to 2.
The table below shows some of the values of y = 2x2 − 6 for values of x from –3 to 2.
| x | – 3 | – 2 | – 1 | 0 | 1 | 2 |
| y = 2x2 − 6 | 2 | – 4 | – 6 | 2 |
Complete the table above.
On the graph paper opposite, draw the graph of y = 2x2 − 6 for values of x
from –3 to 2.
Also involves Substitution into formulae
The table below shows some of the values of y = 2x2 + x + 3 for values of x from –2 to 3.
| x | –2 | –1 | 0 | 1 | 2 | 3 |
| y = 2x2 + x + 3 | 4 | 3 | 6 | 24 |
Complete the table by finding the values of y for x = –2 and for x = 2.
The table below shows some of the values of y = 2x2 + 5x − 3 for values of x from −4 to 2.
| x | −4 | −3 | −2 | −1 | 0 | 1 | 2 |
| y = 2x2 + 5x − 3 | 9 | 0 | −5 | −6 | −3 | 15 |
Complete the table above.
On the graph paper opposite, draw the graph of y = 2x2 + 5x − 3 for values of x from
− 4 to 2.
The table below shows some of the values of y = 2x2 + 5x − 3 for values of x from −4 to 2.
| x | −4 | −3 | −2 | −1 | 0 | 1 | 2 |
| y = 2x2 + 5x − 3 | 9 | 0 | −5 | −6 | −3 | 15 |
Complete the table above.
On the graph paper opposite, draw the graph of y = 2x2 + 5x − 3 for values of x from
− 4 to 2.
The table below shows some of the values of y = x2 + 4x + 5 for values of x from –4 to 1.
| x | –4 | –3 | –2 | –1 | 0 | 1 |
| y = x2 + 4x + 5 | 5 | 2 | 2 | 5 |
Complete the table by finding the value of y for x 
–2 and for x 
1.
On the graph paper below, draw the graph of y = x2 + 4x + 5 for values of x
from –4 to 1.
The table below shows some of the values of y = x2 + 4x + 5 for values of x from –4 to 1.
| x | –4 | –3 | –2 | –1 | 0 | 1 |
| y = x2 + 4x + 5 | 5 | 2 | 2 | 5 |
Complete the table by finding the value of y for x 
–2 and for x 1.
On the graph paper below, draw the graph of y = x2 + 4x + 5 for values of x
from –4 to 1.
Factorise 8x2 
18.
Hence solve 8x2 
18 
0.
Hence, sketch the graph of y 
8x2 
18 on the axes below.
Mark clearly the coordinates of any point where this graph crosses an axis.
Space for working:
The table below shows some of the values of y 
x2 
x 4 for values of x from –3 to 3.
| x | –3 | –2 | –1 | 0 | 1 | 2 | 3 |
y  x2  x  4 | 2 | –2 | – 4 | 2 | 8 |
Complete the table by finding the values of y for x = –1 and for x = 1.
On the graph paper opposite, draw the graph of y 
x2 
x 
4 for values of x from
–3 to 3.
The table below shows some of the values of y x2 x 4 for values of x from –3 to 3.
| x | –3 | –2 | –1 | 0 | 1 | 2 | 3 |
| y x2 x 4 | 2 | –2 | – 4 | 2 | 8 |
Complete the table by finding the values of y for x = –1 and for x = 1.
Complete the table below.
Draw the graph of y = 7 − x2 for values of x between −2 and 4.
Use the graph paper below.
| x | −2 | −1 | 0 | 1 | 2 | 3 | 4 |
| y = 7 − x2 | 3 | 7 | 6 | 3 | −9 |
Complete the table below.
Draw the graph of y = 7 − x2 for values of x between −2 and 4.
Use the graph paper below.
| x | −2 | −1 | 0 | 1 | 2 | 3 | 4 |
| y = 7 − x2 | 3 | 7 | 6 | 3 | −9 |
The table below shows some of the values of y = x2 − 4x − 3 for values of x from –2 to 5.
| x | −2 | –1 | 0 | 1 | 2 | 3 | 4 | 5 |
| y = x2 − 4x − 3 | 2 | −3 | −6 | −6 | −3 | 2 |
Complete the table by finding the value of y for x = −2 and the value of y for x = 2.
On the graph paper opposite, draw the graph of y = x2 − 4x − 3 for values of x from
–2 to 5.
Draw the line y = 1 on the graph paper.
Write down the values of x where the line y = 1 cuts the curve y = x2 − 4x − 3.
Values of x are........ and........
The table below shows some of the values of y = x2 − 4x − 3 for values of x from –2 to 5.
| x | −2 | –1 | 0 | 1 | 2 | 3 | 4 | 5 |
| y = x2 − 4x − 3 | 2 | −3 | −6 | −6 | −3 | 2 |
Complete the table by finding the value of y for x = −2 and the value of y for x = 2.
On the graph paper opposite, draw the graph of y = x2 − 4x − 3 for values of x from
–2 to 5.
Draw the line y = 1 on the graph paper.
Write down the values of x where the line y = 1 cuts the curve y = x2 − 4x − 3.
Values of x are........ and........
The table below shows some of the values of y = x2 − 2x − 4 for values of x from –3 to 4.
| x | −3 | −2 | −1 | 0 | 1 | 2 | 3 | 4 |
| y = x2 − 2x − 4 | 11 | 4 | −1 | −4 | −4 | –1 | 4 |
Complete the table by finding the value of y when x = 1.
On the graph paper opposite, draw the graph of y = x2 − 2x − 4 for values of x from
–3 to 4.
Draw the line y + x = 4 on the graph paper.
Complete the table below.
Draw the graph of y = 3x2 – 25 for values of x between −3 and 4. Use the graph paper below.
You must choose a suitable scale for the y-axis.
| x | –3 | –2 | –1 | 0 | 1 | 2 | 3 | 4 |
| y = 3x2 – 25 | 2 | –22 | –25 | –22 | –13 | 2 | 23 |
The table below shows some of the values of y = x2 + 4x − 1 for values of x from –5 to 2.
| x | –5 | – 4 | –3 | –2 | –1 | 0 | 1 | 2 |
| y = x2 + 4x − 1 | 4 | –1 | – 4 | – 4 | –1 | 4 |
Complete the table by finding the value of y for x = –2 and for x = 2.
On the graph paper opposite, draw the graph of y = x2 + 4x − 1 for values of x from
–5 to 2.
The table below shows some of the values of y = x2 + 4x − 1 for values of x from –5 to 2.
| x | –5 | – 4 | –3 | –2 | –1 | 0 | 1 | 2 |
| y = x2 + 4x − 1 | 4 | –1 | – 4 | – 4 | –1 | 4 |
Complete the table by finding the value of y for x = –2 and for x = 2.
On the graph paper opposite, draw the graph of y = x2 + 4x − 1 for values of x from
–5 to 2.
Draw the line y = 2 on the graph paper.
Write down the values of x where the line y = 2 cuts the curve y = x2 + 4x − 1.
Values of x are........ and........
The sketch above can represent only one of the equations given below.
Circle this equation.
The sketch above can represent only one of the equations given below.
Circle this equation.
Each of the two graphs below is described by one of the equations on the right.
Put a tick in the box next to the equation which correctly describes each graph.
The table below shows some of the values of y = x2 – 5x + 2, for values of x from –1 to 5.
Draw the line y = –3 on the graph paper.
Write down the values of x where the line y = –3 cuts the curve y = x2 – 5x + 2.
Give your answers correct to 1 decimal place.
Also involves Substitution into formulae
The table below shows some of the values of y = x2 – 5x + 2, for values of x from –1 to 5.
Complete the table above.
On the graph paper below, draw the graph of y = x2 – 5x + 2 for values of x from
Draw the line y = –3 on the graph paper.
Write down the values of x where the line y = –3 cuts the curve y = x2 – 5x + 2.
Give your answers correct to 1 decimal place.
Memes
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