Using quadratic graphs Revision Notes for Edexcel GCSE Maths

Using quadratic graphs

What are quadratic graphs?

Quadratic graphs are curved graphs that represent quadratic equations containing an x² term. These graphs have a distinctive U-shape (or upside-down U) called a parabola. You'll often need to read values from these graphs or use them to solve quadratic equations.

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Quadratic graphs always form smooth, symmetrical curves. The shape depends on whether the coefficient of x² is positive (U-shape opening upward) or negative (upside-down U opening downward).

Reading values from quadratic graphs

There are two main ways to read values from a quadratic graph:

Looking at crossing points - where the graph crosses the x-axis or y-axis
Drawing horizontal lines - to find specific y-values on the graph

Creating and using a table of values

When drawing a quadratic graph, you should always use a table of values first. This helps you plot accurate points before drawing the curve.

Steps to complete a table of values:

Choose x-values (usually given in the question)
Substitute each x-value into the quadratic equation
Calculate the corresponding y-values
Record your results in the table

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Worked Example: Using a Table of Values

For the equation $y = x^2 - x - 3$

When $x = -2$ : $y = (-2)^2 - (-2) - 3 = 4 + 2 - 3 = 3$ When $x = 0$ : $y = (0)^2 - (0) - 3 = 0 - 0 - 3 = -3$

Drawing quadratic graphs correctly

Key rules for drawing quadratic graphs:

Use a smooth curve - never use a ruler to join the points
Plot all points accurately first, then draw the curve through them
Make sure the curve is symmetrical - quadratic graphs have a line of symmetry
Extend the curve slightly beyond your plotted points if needed

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Common Mistake to Avoid: Never use a ruler to connect the points on a quadratic graph. Quadratic graphs must always be smooth, curved lines. Using straight lines between points will lose you marks in exams.

Finding solutions from quadratic graphs

The solutions (or roots) of a quadratic equation are the x-coordinates where the graph crosses the x-axis. These are the values of x when $y = 0$ .

To find solutions:

Look for where the curve crosses the x-axis
Read down to find the x-coordinates at these crossing points
Read to the nearest small square on the grid for accuracy
Write your answers to 1 decimal place unless told otherwise

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Worked Example: Finding Solutions

If the graph crosses the x-axis at $x = -1.3$ and $x = 2.3$ , then these are the solutions to the equation.

This means the quadratic equation equals zero when $x = -1.3$ or $x = 2.3$ .

Using horizontal lines to find values

When you need to find the values of x for a specific y-value, draw a horizontal line across the graph.

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Method for Using Horizontal Lines:

Draw a horizontal line at the required y-value
Mark where this line crosses the quadratic curve
Read down to the x-axis to find the x-coordinates
These x-values are your answers

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Worked Example: Finding x-values for a Given y-value

To find where $y = 8$ , draw a horizontal line at $y = 8$ and read where it crosses the curve. The x-coordinates at these intersection points are your answers.

Important exam tips

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Essential Exam Guidelines:

Don't use a ruler - quadratic graphs must be smooth curves, not straight lines between points
Read accurately - always read to the nearest small square on the grid
Show your working - include your table of values and any horizontal lines you draw
Check your curve shape - it should be a smooth U-shape or upside-down U

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Key Points to Remember:

Quadratic graphs are U-shaped curves that represent equations with $x^2$ terms
Always complete a table of values before plotting the graph
Solutions are found where the graph crosses the x-axis
Use horizontal lines to find x-values for specific y-values
Draw smooth curves without a ruler and read to the nearest small square for accuracy

Using quadratic graphs (Edexcel GCSE Maths): Revision Notes