How can you find the coordinates of the turning point of a quadratic graph?

To find the coordinates of the turning point of a quadratic graph, you can either: complete the square differentiate and set the derivative equal to zero to find the x -coordinate

True or False? You should always use a ruler when plotting the graph of a function.

False. You should only use a ruler if a graph is linear (and for drawing the axes if they are not given). For curves, draw a single smooth freehand curve .

IGCSEMathsEdexcelMaths A (Modular)Higher Unit 1FlashcardsGraphs & CoordinatesGraphs of Functions

Graphs of Functions (Edexcel IGCSE Maths A (Modular)) Flashcards

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FrontTypes of Graphs
Why does the graph of $y = \frac{1}{x}$ not touch the y-axis?

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Why does the graph of $y = \frac{1}{x}$ not touch the y-axis?
The graph of $y = \frac{1}{x}$ not touch the y-axis because on the y-axis, $x = 0$ . You cannot divide by zero therefore the graph does not have any values on the y-axis.
What is an asymptote?
An asymptote is a line on a graph that a curve gets closer and closer to but never touches.
These may be horizontal or vertical.
E.g. $y = \frac{1}{x}$ has asymptotes at $y = 0$ and $x = 0$ .
How many turning points does the graph of a cubic have?
The graph of a cubic has two turning points; a minimum and a maximum.
However, note that $y = \pm x^{3}$ does not have any turning points.
Will the vertex of the graph $y = - x^{2} + x + 5$ be a maximum or a minimum point?
The vertex of the graph $y = - x^{2} + x + 5$ will be a maximum point.
The vertex of a quadratic graph will be a maximum point if the coefficient of $x^{2}$ is negative. The graph is n-shaped.
Where does the graph of $y = 3 (x - 1) (x + 2)$ cross the x-axis?
The graph of $y = 3 (x - 1) (x + 2)$ crosses the x-axis at $(1, 0)$ and $(- 2, 0)$ .
To find these roots, make each factor equal to zero to find the x-coordinate:
- $x - 1 = 0$ gives $x = 1$
- $x + 2 = 0$ gives $x = - 2$
How can you find the coordinates of the turning point of a quadratic graph?
To find the coordinates of the turning point of a quadratic graph, you can either:
- complete the square
- differentiate and set the derivative equal to zero to find the x-coordinate
True or False?
The turning point of $y = 4 - {(x - 1)}^{2}$ is at the point $(4, 1)$ .
False.
The turning point of $y = 4 - {(x - 1)}^{2}$ is not at the point $(4, 1)$ .
The x-coordinate is the value that makes the squared bracket equal to zero.
The coordinates should be $(1, 4)$ .
True or False?
You should always use a ruler when plotting the graph of a function.
False.
You should only use a ruler if a graph is linear (and for drawing the axes if they are not given).
For curves, draw a single smooth freehand curve.
How would you find the y-intercept of a graph using its equation?
To find the y-intercept of a graph, you would substitute $x = 0$ into the equation.
True or False?
The solutions to $x^{3} - 4 x = 0$ are the value(s) where the graph of $y = x^{3} - 4 x$ crosses the y-axis.
False.
The solutions to $x^{3} - 4 x = 0$ are not the value(s) where the graph of $y = x^{3} - 4 x$ crosses the y-axis.
$x^{3} - 4 x = 0$ when $y = 0$ which is the x-axis. Therefore the solutions are the values where the graph crosses the x-axis.
The solutions of $x^{3} + x^{2} - 3 = x - 2$ are the x values of the intersections between $y = x^{3} + x^{2} - 3$ and which other graph?
The solutions of $x^{3} + x^{2} - 3 = x - 2$ are the x values of the intersections between $y = x^{3} + x^{2} - 3$ and $y = x - 2$ .
True or False?
The x values of the intersections of the two graphs $y = x + 1$ and $y = x^{2} + 5 x + 4$ are the solutions of $x^{2} + 4 x + 3 = 0$ .
True.
The x values of the intersections of the two graphs $y = x + 1$ and $y = x^{2} + 5 x + 4$ are the solutions of $x^{2} + 4 x + 3 = 0$ .
Set the equations equal to each other and rearrange: $x^{2} + 5 x + 4 = x + 1$ .
What is the graph of $y = \sin x$ for $- 360 ° \leq x \leq 360 °$ ?
The graph of $y = \sin x$ for $- 360 ° \leq x \leq 360 °$ is:
What is the graph of $y = \cos x$ for $- 360 ° \leq x \leq 360 °$ ?
The graph of $y = \cos x$ for $- 360 ° \leq x \leq 360 °$ is:
What is the graph of $y = \tan x$ for $- 360 ° \leq x \leq 360 °$ ?
The graph of $y = \tan x$ for $- 360 ° \leq x \leq 360 °$ is:
True or False?
The point $(0, 0)$ lies on the graph $y = \sin x$ .
True.
The point $(0, 0)$ lies on the graph $y = \sin x$ .
What is the y-intercept of the graph $y = \cos x$ ?
The y-intercept of the graph $y = \cos x$ is $(0, 1)$ .
What is the minimum y value of the graph $y = \sin x$ ?
The minimum y value of the graph $y = \sin x$ is -1.
True or False?
The graph $y = \cos x$ repeats itself every 180°.
False.
The graph $y = \cos x$ does not repeat itself every 180°.
It repeats itself every 360°.
True or False?
The graph $y = \tan x$ repeats itself every 180°.
True.
The graph $y = \tan x$ repeats itself every 180°.
The graph $y = \sin x$ repeats itself every how many degrees?
The graph $y = \sin x$ repeats itself every 360°.
True or False?
The maximum y value on the graph $y = \tan x$ is 1.
False.
The maximum y value on the graph $y = \tan x$ is not 1.
The graph $y = \tan x$ does not have a maximum value.

Graphs of Functions (Edexcel IGCSE Maths A (Modular)) Flashcards

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Number

Number Toolkit

Set Notation & Venn Diagrams

Powers & Roots

Fractions

Fractions, Decimals & Percentages

Rounding, Estimation & Bounds

Surds

Using a Calculator

Exchange Rates & Best Buys

Algebra

Algebra Toolkit

Algebraic Roots & Indices

Expanding Brackets

Factorising

Completing the Square

Algebraic Fractions

Solving Linear Equations

Solving Quadratic Equations

Graphs & Coordinates

Coordinate Geometry

Linear Graphs y = mx + c

Graphs of Functions

Real-Life Graphs

Shape, Space & Measure

Standard & Compound Units

Area & Perimeter

Circles, Arcs & Sectors

Properties of 3D Shapes

Trigonometry

Right-Angled Triangles: Pythagoras & Trigonometry

Sine, Cosine Rule & Area of Triangles

3D Pythagoras & Trigonometry

Statistics & Probability

Histograms

Probability Toolkit

Probability Diagrams: Venn & Tree Diagrams

Combined & Conditional Probability