Quadratic graphs Revision Notes for Edexcel GCSE Maths

Quadratic graphs

What are quadratic equations?

A quadratic equation includes a term with x². When you plot these equations on a graph, they create curved lines rather than straight ones. You can draw these graphs by working out a table of values first, then plotting the points carefully.

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The most important feature of any quadratic graph is the turning point - this is where the curve changes direction, either from going up to going down, or from going down to going up.

Working with quadratic graphs

Creating a table of values

To draw a quadratic graph, you need to substitute different x-values into your equation to find the corresponding y-values. Let's look at how this works:

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Worked Example: Creating a table of values

For the equation $y = 4x - x^2$ :

When you substitute values:

For $x = -1$ : Calculate $4(-1) - (-1)^2 = -4 - 1 = -5$
For $x = 4$ : Calculate $4(4) - (4)^2 = 16 - 16 = 0$

Work through each x-value systematically to complete your table.

Plotting your graph

Once you have your table of values complete, follow these essential steps:

Plot each point carefully on your graph paper
Join the points with a smooth curve - never use straight lines between points
Label your graph with the equation
Mark the turning point coordinates if asked

Checking your work

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All points should lie perfectly on your smooth curve. If a point doesn't fit, double-check your calculation for that x-value before continuing.

Drawing techniques for quadratic curves

Essential steps for accurate graphs

When creating quadratic graphs, these techniques will ensure accuracy:

Use a sharp pencil for precise plotting
Plot points carefully - accuracy is crucial for full marks
Draw smooth curves that pass through every plotted point
Label your graph with the equation
Identify the curve shape - it will be either U-shaped or an upside-down U

Drawing smooth curves effectively

Making your curve smooth can be tricky.

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A helpful technique is to turn your graph paper so your hand moves naturally inside the curve as you draw. This makes it easier to create that perfect smooth line.

Recognising quadratic graph shapes

Quadratic graphs always form one of two distinct shapes:

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Graph Shapes:

U-shaped (opens upwards) - when the $x^2$ term is positive
Upside-down U-shaped (opens downwards) - when the $x^2$ term is negative

The turning point is always at the bottom of a U-shape or the top of an upside-down U-shape.

Exam tips

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Essential Exam Strategies:

Complete tables methodically - work through each column carefully
Check your arithmetic - calculation errors lose marks easily
Plot points precisely - use the grid lines to be accurate
Draw smooth curves only - jagged lines between points lose marks
Read coordinates carefully from your graph when asked

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Key Points to Remember:

Quadratic equations contain x² terms and create curved graphs
Always complete a table of values before plotting
The turning point shows where the curve changes direction
Use smooth curves, never straight lines between points
Check all plotted points lie on your final curve

Quadratic graphs (Edexcel GCSE Maths): Revision Notes