Chapter 4 Graphs And Transformations - Year 1 Flashcards
Draw the shape of a quadratic with a positive x^2 coefficient
It starts going down and ends going up
Describe the shape of a graph with a negative x^2 coefficient
It starts going up end ends going down
Describe the shape of a graph with a positive x^3 coefficient
It starts going up and ends going up with a relapse in the middle
Describe the shape of a graph with a negative x^3 coefficient
It starts going down and ends going down
Describe the shape of a graph with a positive x^4 coefficient
W shape
Describe the shape of a graph with a negative x^4 coefficient
M shape
Describe the graph of y=x^2
Describe the graph y=x^3
Describe the graph y=x^4
A longer y=x^2
How do you sketch a graph?
Write shape, roots and y intercept down the side of your page
Work out if the highest power of x will be positive or negative then sketch a general shaoemof the graph next to the word shape
Calculate the roots of the equation (factorise)
Calculate the y intercept
Then draw the graph labelling where the graph cut the x and y axis
What do you do in case of a double root?
The graph does a double turn when it gets to the cutting point
What happens if there is a triple root?
There will be a point of inflexion
How do you sketch a cubic that only has 1 real root?
How do you know if it only has 1 real root?
You know that the cubic only has 1 real root if the equation is given in the form (x+d)(ax^2+bx+c) and the quadratic has a discriminant that is less than 0
Since it only has 1 real root the graph must have a point of inflexion because…
Gubihbdijdosjbvfsojbvrwjivbrwojvrojvnejo v
How can you work out the equation of a cubic or quartic equation if you are given all the points the graph crosses the x axis?
You say reverse the sign and put it into the factorised form of an equation
Then expand it
Eg x=2 x=3 x=-1
(x-2)(x-3)(x+1).
If a question asks you to state the value of a, b and c what may be unique about it and how would you answer?
b may be for the x^2 term but there may be no x^2 term in which case b=0
How do you calculate the y intercept?
Make all x values 0
The y intercept will be the value without an x attacked to it
What does a quartic with a triple root look like?
It has a point of inflexion
What do all reciprocal graphs have in common?
There are graphs in two commons
In which sectors will a positive x reciprocal graph be in?
1,3
In which sectors will a negative x reciprocal graph be in?
2,4
In which sectors will a negative x^2 reciprocal graph be in?
3,4
In which sectors will a positive x^2 reciprocal graph be in?
1,2
What happens as the numerator (in a reciprocal graph gets) bigger?
The space underneath the graph and above the axis gets larger
The asymtope will never change because of this
What is the asymptote?
The line that the graph approaches but never reaches
What will the equations of the asymptotes normally be?
x=0
y=0
What do we know about the gradient of a cubic and quadratic?
The gradient of the cubic will always be greater than the quadratic
Ina reciprocal graph how does the denominator change the graph
Unless it is + or - a number it doesn’t
Graphs with a dominator of 2x and x will be the same if the numerator is the same
In a graph what should you always lable
Where it crosses the axis
Draw a dot where the points of insertion are
How do you find where two lines intercept?
Solve the equations simultaneously
Which axis does a change inside the brackets effect?
What do we expect?
X axis
Do the opposite
What axis does a change outside the brackets effect?
What do we expect?
Y
What we expect
What do we do for the transformation f(ax)?
Divide all the x axis by a
What do we do for the transformation af(x)?
Multiply all the y axis by a
4.5/4.7 questions……
It the question gives you a maximum point. Then tells you that a transformation of f(x)+k has happened what do you do?
Find the difference between the different co-ordinate points
What is the first key tip for drawing graphs?
Sketch the axis of the graphs in a different colour
Is:
Sqr x =-2 a real solution
Why?
No
The sqr of x can’t be negative
If it tells you to only plot 1 graph what doesn’t matter?
The magnitude. (Relative to other graphs. Only the general shale of the graph matters)
