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
