01 Quadratics Flashcards
If a quadratic has an positive x², will there be a maximum or minimum point?
Minimum point
If a quadratic has an -x², will there be a maximum or minimum point?
Maximum
Where is the line of symmetry in a quadratic graph?
A vertical line through the min/max point
What is the vertex?
The turning point
How do you find the min/max point from completing the square? Use y = (x + a)² +b
(-a,b) change the sign of a for x and leave b the same as y.
What is the discriminant?
b²-4ac
If the discriminant of a quadratic is more than zero than how many real roots does it have?
2
If the discriminant of a quadratic is equal to zero than how many real roots does it have?
1
If the discriminant of a quadratic is less than zero than how many real roots does it have?
None
What type of equation should you use to find intersection points of 2 graphs?
Simultaneous
Where is the line of symmetry on a quadratic curve?
A vertical line through the min / max point.
If the discriminant is above 0 how many intersection points are there?
2
If the discriminant is equal to 0 how many intersection points does it have?
1
If the discriminant is less than 0 how many intersection points are there?
0
How do you use the discriminant to find how many intersection points of a quadratic curve and a line there are?
Use a simultaneous equation then use the discriminant
What does this mean?
A and B
What does this mean?
A or B
What does this mean?
The empty set
What does this mean?
A set of all real numbers (including all possible decimals)
What does this mean?
A set of all integers (including negative numbers or 0)
What does this mean?
A set of all natural numbers (all positive integers)
What does this mean?
x is a member of set A.
What does this mean?
x is a real number.
How do you rearrange quadratic inequalities?
- Rearrange so the right hand side is 0
- Solve the quadratic equation to fin the critical values
- Sketch the graph of the quadratic function
- Use the graph to find the required set of values.
When does a cubic graph look like this?
When all 3 roots are the same (positive).
When does a cubic graph look like this?
When you have 3 different roots. (Positive)
When does a cubic graph look like this?
When you have 1 repeated root and one different root. (Positive)
When does a cubic graph look like this?
All 3 roots are the same (negative).
When does a cubic graph look like this?
3 different roots (negative).
When does a cubic graph look like this?
One repeated root and one different.
What is an a^x graph called?
An exponential function
What does an exponential graph look like (y = a^x)?
What type of graph is y = k/x (or y=k/x^2)?
A reciprocal graph
What type of graph is this?
Reciprocal (y=k/x)
Where are the asymptotes on a reciprocal graph?
X=0 and y=0
What is an asymptote?
A line which the graph approaches but never reaches.
What type of graph is this?
A reciprocal graph (y=k/x^2)
What type of graph is this?
A reciprocal graph (y=k/x^2)
