How can you recognise the graph of a cubic function?

A cubic curve can change direction twice , which gives it a double bend. A positive cubic runs uphill from bottom left to top right, and a negative cubic runs downhill from top left to bottom right.

Define the vertex of a quadratic graph.

The vertex is the point where the curve changes direction. Every quadratic graph has exactly one vertex.

True or False? A curved graph drawn from a table of values should be joined up using a ruler.

False. A curve must be drawn as a single smooth freehand curve passing through all the plotted points. A ruler is only for straight-line graphs, and using one on a curve produces a series of straight segments instead.

How accurately should each point be plotted on the grid?

Mark each point with a cross , positioned to within half of the smallest square on the grid. A point plotted more roughly than that can pull the whole curve out of shape.

GCSEMathsEdexcelFoundationFlashcardsAlgebraGraphs of Functions

Graphs of Functions (Edexcel GCSE Maths: Foundation): Flashcards

Exam code: 1MA1

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FrontTypes of Graphs
How can you tell from its equation whether a graph is a straight line, a quadratic or a cubic?

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Cards in this collection (17)

How can you tell from its equation whether a graph is a straight line, a quadratic or a cubic?
Look at the highest power of $x$ in the equation.
A highest power of $1$ gives a straight line, a highest power of $2$ gives a quadratic curve, and a highest power of $3$ gives a cubic curve.
Complete the two descriptions by filling in the missing words:
The graph of $y = 4$ is a $______$ line.
The graph of $x = 2$ is a $______$ line.
The completed descriptions are:
The graph of $y = 4$ is a horizontal line.
The graph of $x = 2$ is a vertical line.
Any equation of the form $y = c$ gives a horizontal line, and any of the form $x = k$ gives a vertical one.
What shape is the graph of $y = a x^{2} + b x + c$ , and what decides which way up it is?
It is a parabola, which is either a u-shape or an n-shape.
The sign of the number in front of $x^{2}$ decides which: positive gives a u-shape, and negative gives an n-shape.
How can you recognise the graph of a cubic function?
A cubic curve can change direction twice, which gives it a double bend.
A positive cubic runs uphill from bottom left to top right, and a negative cubic runs downhill from top left to bottom right.
What does the graph of $y = \frac{1}{x}$ look like?
It has two separate curved branches.
The two branches never join up, so the graph is in two pieces rather than one continuous curve.
True or False?
The graph of $x = - 1$ is a straight line.
True.
Every point on it has an $x$ -coordinate of $- 1$ , and those points form a straight line.
An equation does not have to begin with $y =$ in order to describe a line.
Define the vertex of a quadratic graph.
The vertex is the point where the curve changes direction.
Every quadratic graph has exactly one vertex.
Complete the pair of statements by filling in the missing words:
A positive quadratic has a $______$ point at its vertex.
A negative quadratic has a $______$ point at its vertex.
The completed statements are:
A positive quadratic has a minimum point at its vertex.
A negative quadratic has a maximum point at its vertex.
What are the roots of a quadratic graph?
The roots are the $x$ -intercepts: the values of $x$ where the curve meets the $x$ -axis.
A curve that crosses the axis has two roots, and one that just touches it has only one.
True or False?
A quadratic graph that never touches the $x$ -axis still crosses the $y$ -axis.
True.
Every quadratic graph crosses the $y$ -axis exactly once, whatever it does at the $x$ -axis.
A curve sitting entirely above the $x$ -axis still has a $y$ value when $x = 0$ .
What is the equation of the line of symmetry of a quadratic graph?
It is a vertical line with equation $x = k$ .
Here $k$ is the $x$ -coordinate of the vertex, so the line of symmetry passes straight through the turning point.
A quadratic graph crosses the $x$ -axis at $x = 2$ and $x = 3$ . What is the equation of its line of symmetry?
The line of symmetry is $x = 2.5$ .
The roots are symmetric about it, so it lies exactly halfway between them.
How do you complete a table of values for the graph of $y = 10 - 8 x^{2}$ ?
Substitute each $x$ value from the table into the equation to work out the matching $y$ value.
For $x = - 1.5$ this gives $y = 10 - 8 \times 2.25 = - 8$ .
Complete two more values from the table for $y = 10 - 8 x^{2}$ :
When $x = 0$ , $y =______$ .
When $x = 1$ , $y =______$ .
The completed values are:
When $x = 0$ , $y = 10$ .
When $x = 1$ , $y = 2$ .
True or False?
A curved graph drawn from a table of values should be joined up using a ruler.
False.
A curve must be drawn as a single smooth freehand curve passing through all the plotted points.
A ruler is only for straight-line graphs, and using one on a curve produces a series of straight segments instead.
How accurately should each point be plotted on the grid?
Mark each point with a cross, positioned to within half of the smallest square on the grid.
A point plotted more roughly than that can pull the whole curve out of shape.
When making a table of values for $y = \frac{1}{x}$ , why is there no $y$ value to write in the $x = 0$ column?
Because $1$ divided by $0$ has no value: division by zero is not allowed, and a calculator returns an error.
Leave that column blank and plot no point there.

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