Plotting Quadratic Graphs

Here we will learn about plotting quadratic graphs including how to substitute values to create a table and then draw the graph of a quadratic function from this table.

There are also quadratic graphs worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What is plotting quadratic graphs?

Plotting quadratic graphs is drawing up a table of values for the x and y coordinates, and then plotting these on a set of axes.

Quadratic graphs are graphs of quadratic functions – that is, any function which has x^2 as its highest power.

E.g.

y=x^{2}+2 x+5 is a quadratic function.

In order to complete a table of values, we substitute each x value into the quadratic function to obtain the matching y value. Each one of these is a coordinate pair. For the function y=x^{2}+2 x+5 , the table of values from x=-3 to x=2 would look like this:

\begin{aligned} &x \quad \quad -3 \quad \quad -2 \quad \quad -1 \quad \quad \quad 0 \quad \quad \quad 1 \quad \quad \quad 2 \\ &y \quad \quad \quad 8 \quad \quad\quad 5 \quad \quad \quad 4 \quad \quad \quad 5 \quad \quad \quad 8 \quad \quad \quad 13 \end{aligned}

and the graph would look like this:

Plotting quadratic graphs image 1 1

The shape made by the graph of a quadratic function is called a parabola, and is symmetric.

What is plotting quadratic graphs?

What is plotting quadratic graphs?

How to plot a quadratic graph

In order to plot a graph of a quadratic function:

  1. Draw a table of values, and substitute x values to find matching y values.
  2. Plot these coordinate pairs on a graph.
  3. Join the points with a smooth curve.

Explain how to plot a quadratic graph

Explain how to plot a quadratic graph

Plotting quadratic graphs worksheet

Plotting quadratic graphs worksheet

Plotting quadratic graphs worksheet

Get your free plotting quadratic graphs worksheet of 20+ questions and answers. Includes reasoning and applied questions.

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Plotting quadratic graphs worksheet

Plotting quadratic graphs worksheet

Plotting quadratic graphs worksheet

Get your free plotting quadratic graphs worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREE

Related lessons on quadratic graphs

Plotting quadratic graphs is part of our series of lessons to support revision on types of graphs. You may find it helpful to start with the main quadratic graphs lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

Plotting quadratic graphs examples

Example 1: the standard quadratic graph

Draw the graph of

y=x^{2}

  1. Draw a table of values, and substitute x values to find matching y values.

You will usually be given the range of values to use for x . Sometimes this might be written as ‘from -3 to 3 ’, or you may see it written symbolically as -3 ≤ x ≤ 3 .

\begin{aligned} &x \quad \quad -3 \quad \quad -2 \quad \quad -1 \quad \quad \quad 0 \quad \quad \quad 1 \quad \quad \quad 2 \quad \quad \quad 3 \\ &y \quad \quad \quad 9 \quad \quad\quad 4 \quad \quad \quad 1 \quad \quad \quad 0 \quad \quad \quad 1 \quad \quad \quad 4 \quad \quad \quad 9 \end{aligned}

When:

\begin{aligned} &x=-3, \;y=(-3)^{2}=9 \\\\ &x=-2,\; y=(-2)^{2}=4 \\\\ &x=-1, \;y=(-1)^{2}=1 \end{aligned}

And so on…

2Plot these coordinate pairs on a graph.

Plotting quadratic graphs example 1 step 2 1

3Join the points with a smooth curve.

Plotting quadratic graphs example 1 step 3 1

Example 2: a simple quadratic

Draw the graph of

y=x^{2}-4

Draw a table of values, and substitute x values to find matching y values.

Plot these coordinate pairs on a graph.

Join the points with a smooth curve.

Example 3: another simple quadratic

Draw the graph of

y=x^{2}+3x

Draw a table of values, and substitute x values to find matching y values.

Plot these coordinate pairs on a graph.

Join the points with a smooth curve.

Example 4:  a quadratic trinomial (three parts)

Draw the graph of

y=x^{2}+3x+2

Draw a table of values, and substitute x values to find matching y values.

Plot these coordinate pairs on a graph.

Join the points with a smooth curve.

Example 5: dealing with negative terms

Draw the graph of

y=x^{2}-2x+4

Draw a table of values, and substitute x values to find matching y values.

Plot these coordinate pairs on a graph.

Join the points with a smooth curve.

Example 6: coefficient of x2 ≠ 1

Draw the graph of

y=2x^{2}+3x-5

Draw a table of values, and substitute x values to find matching y values.

Plot these coordinate pairs on a graph.

Join the points with a smooth curve.

Example 7: coefficient of x2 ≠ 1 , negative x2 term

Draw the graph of

y=-2x^{2}-4x+3

Draw a table of values, and substitute x values to find matching y values.

Plot these coordinate pairs on a graph.

Join the points with a smooth curve.

Common misconceptions

  • Drawing a pointy vertex

Make sure that the vertex of the graph is a smooth curve, not pointed:

Plotting quadratic graphs Common Misconceptions 1 1

  • Making errors when dealing with negative x values, particularly when squaring

E.g.

(-3)^{2}=9 , not -9 .

If you’re using your calculator, make sure you include brackets around the x value that you are squaring.

Practice plotting quadratic graphs questions

1. Draw the graph of:

 

y=x^{2}+4

Plotting quadratic graphs Practice questions 1a 1

GCSE Quiz False

Plotting quadratic graphs Practice questions 1b 1

GCSE Quiz False

Plotting quadratic graphs Practice questions 1c 1

GCSE Quiz False

Plotting quadratic graphs Practice questions 1d 1

GCSE Quiz True

The y -intercept is (0,4) and the graph is a u shape because the x^2 coefficient is positive.

2. Draw the graph of:

 

y=x^{2}+4x

Plotting quadratic graphs Practice questions 2a 1

GCSE Quiz True

Plotting quadratic graphs Practice questions 2b 1

GCSE Quiz False

Plotting quadratic graphs Practice questions 2c 1

GCSE Quiz False

Plotting quadratic graphs Practice questions 2d 1

GCSE Quiz False

The quadratic factorises to give x(x+4) so the roots are x=0 and x=-4.

3. Draw the graph of:

 

y=x^{2}-6x

Plotting quadratic graphs Practice questions 3a 1

GCSE Quiz False

Plotting quadratic graphs Practice questions 3b 1

GCSE Quiz True

Plotting quadratic graphs Practice questions 3c 1

GCSE Quiz False

Plotting quadratic graphs Practice questions 3d 1

GCSE Quiz False

The quadratic factorises to give x(x-6) so the roots are x=0 and x=6 .
 
The graph is a u shape because the x^2 coefficient is positive.

4. Draw the graph of:

 

y=x^{2}+2x+3

Plotting quadratic graphs Practice questions 4a 1

GCSE Quiz False

Plotting quadratic graphs Practice questions 4b 1

GCSE Quiz False

Plotting quadratic graphs Practice questions 4c 1

GCSE Quiz True

Plotting quadratic graphs Practice questions 4d 1

GCSE Quiz False

The quadratic has no real roots so it doesn’t intersect the x axis.
 
The constant term is 3 so the y intercept is (0,3) . The graph is a u shape because the x^2 coefficient is positive.

5. Draw the graph of:

 

y=x^{2}-5x-3

Plotting quadratic graphs Practice questions 5A 1

GCSE Quiz False

Plotting quadratic graphs Practice questions 5B 1

GCSE Quiz False

Plotting quadratic graphs Practice questions 5C 1

GCSE Quiz False

Plotting quadratic graphs Practice questions 5D 1

GCSE Quiz True

The quadratic has two roots, which could be found by completing the square or using the quadratic formula.
 
The constant term is -3 so the y intercept is (0,-3) .
 
The graph is a u shape because the x^2 coefficient is positive.

6. Draw the graph of:

 

y=2x^{2}+4x-7

Plotting quadratic graphs Practice questions 6A 1

GCSE Quiz False

Plotting quadratic graphs Practice questions 6B 1

GCSE Quiz False

Plotting quadratic graphs Practice questions 6C 1

GCSE Quiz True

Plotting quadratic graphs Practice questions 6D 1

GCSE Quiz False

The quadratic has two roots, which could be found by completing the square or using the quadratic formula.
 
The constant term is -7 so the y intercept is (0,-7) .
 
The graph is a u shape because the x^2 coefficient is positive.

7. Draw the graph of:

 

y=4x-3x^{2}

Plotting quadratic graphs Practice questions 7A 1

GCSE Quiz True

Plotting quadratic graphs Practice questions 7B 1

GCSE Quiz False

Plotting quadratic graphs Practice questions 7C 1

GCSE Quiz False

Plotting quadratic graphs Practice questions 7D 1

GCSE Quiz False

The quadratic factorises to give x(4-3x) so the roots are x=0 and x=\frac{4}{3} .
 
The graph is a n shape because the x^2 coefficient is negative.

Plotting quadratic graphs GCSE questions

1. (a) Complete the table of values for y=x^{2}+4x-2

 

\begin{aligned} &x \quad \quad -6 \quad \quad -5 \quad \quad -4 \quad \quad -3 \quad \quad -2 \quad \quad -1 \quad \quad \quad 0 \quad \quad \quad 1\\\\ &y \quad \quad\;\; 10 \quad \quad \quad \quad \quad\quad\quad\quad\quad-5 \end{aligned}

 

(b) On the grid draw the graph of y=x^{2}+4x-2 for values of x from -6 to 1 .

 

Plotting quadratic graphs GCSE questions 1b 1

 

(4 marks)

Show answer

(a)

 

\begin{aligned} &x \quad \quad -6 \quad \quad -5 \quad \quad -4 \quad \quad -3 \quad \quad -2 \quad \quad -1 \quad \quad \quad 0 \quad \quad \quad 1\\\\ &y \quad \quad\;\; 10 \quad \quad \quad 3 \quad \quad -2 \quad \quad -5 \quad \quad -6 \quad \quad -5 \quad \quad -2 \quad \quad 3 \end{aligned}

(2)

 

(b)

 

Plotting quadratic graphs GCSE questions 1b ans 1

(2)

2. (a) Complete the table of values for y=2+3x-x^{2}

 

\begin{aligned} &x \quad \quad -2 \quad \quad -1 \quad \quad \quad 0 \quad \quad \quad 1 \quad \quad \quad 2 \quad \quad \quad 3 \quad \quad \quad 4 \quad \quad \quad 5\\\\ &y \quad \quad \quad \quad \quad\;\;-2 \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad 2 \end{aligned}

 

(b) Draw the graph of y=2+3x-x^{2} for values of x from -2 to 5 .

 

Plotting quadratic graphs GCSE question 2b 1

 

(4 marks)

Show answer

(a)

 

\begin{aligned} &x \quad \quad -2 \quad \quad -1 \quad \quad \quad 0 \quad \quad \quad 1 \quad \quad \quad 2 \quad \quad \quad 3 \quad \quad \quad 4 \quad \quad \quad 5\\\\ &y \quad \quad -8 \quad \quad -2 \quad \quad \quad 2 \quad \quad \quad 4 \quad \quad \quad 4 \quad \quad \quad 2 \quad \quad -2 \quad \quad -8 \end{aligned}

(2)

 

(b)

 

Plotting quadratic graphs GCSE questions 2b ans 1

(2)

3. (a) Complete the table of values for y=2x^{2}+x-5

 

\begin{aligned} &x \quad \quad -3 \quad \quad -2 \quad \quad -1 \quad \quad \quad 0 \quad \quad \quad 1 \quad \quad \quad 2 \\\\ &y \quad \quad \quad \quad \quad\;\;-1 \quad \quad \quad \quad \quad \quad \quad \quad \quad -2 \end{aligned}

 

(b) On the grid draw the graph of y=2x^{2}+x-5 for values of x from -3 to 2 .

 

Plotting quadratic graphs GCSE questions 3b 1

 

(4 marks)

Show answer

(a)

 

\begin{aligned} &x \quad \quad -3 \quad \quad -2 \quad \quad -1 \quad \quad \quad 0 \quad \quad \quad 1 \quad \quad \quad 2 \\\\ &y \quad \quad \;\; 10 \quad \quad \quad 1 \quad \quad -4 \quad \quad -5 \quad \quad -2 \quad \quad \quad 5 \end{aligned}

(2)

 

(b)

 

Plotting quadratic graphs GCSE questions 3b ans 1

(2)

The next lessons are

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