topic 1 and 2 Flashcards
(30 cards)
How can you solve quadratic equations
factorisation
Completing the square
using the quadratic formula
What is the quadratic formula
x= ______
-b +-√b² - 4ac
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2a
How to solve simultaneous equations where one is linear and one is quadratic
rearrange the linear equation to make either x or y the subject
substitute x or y in the quadratic equation and then solve
for a quadratic function f(x) = ax² + bx + c that is written in the form f(x) = a(x - h)² + k: what is the line of symmetry
the line of symmetry is x = h = - b/2a
for a quadratic function f(x) = ax² + bx + c that is written in the form f(x) = a(x - h)² + k: what is the minimum/maximum point
If a > 0, there is a minimum point at (h, k)
If a < 0, there is a maximum point at (h, k)
what is the discriminant of quadratic equation ax² + bx + c = 0 and corresponding curve y = ax² + bx + c
Discriminant = b² - 4ac
how to calculate the amount of roots in ax² + bx + c = 0
if b² - 4ac > 0, then the equation ax² + bx + c = 0 has two distinct real roots
If b² - 4ac = 0, then the equation ax² + bx + c = 0 has two equal real roots
If b² - 4ac < 0, then the equation has no real roots
What is the condition for a quadratic equation to have real roots
the condition for a quadratic equation to have real roots is
b² - 4ac ≥ 0
what happens if a line and a general quadratic curve interest at one point
Then the line is a target to the curve at that point
what does solving simultaneously the equations for the line and the curve do
It gives an equation of the form ax² + bx + c = 0
What gives information about the intersection of the line and the curve
b² - 4ac
How many distinct points of intersection come with b² - 4ac
if b² - 4ac > 0, two distinct points of intersection
If b² - 4ac = 0, one point of intersection (line is a tangent)
If b² - 4ac < 0, no points of intersection
what is a function
A function is a rule that maps each x value to just one y value for a defined set of input values
what are the two types of functions
A function can be either one-one or many-one
What is the set of input values for a function called
the domain of the function
What is the set of output values for a function called
it is called the range (or image set) of the functions
What does fg(x) mean
The function g acts on x first, then f acts on the result
How does fg exist
it only exists if the range of g is contained within the domain of f
What is the inverse of a function
the inverse of a function f(x) is the function that undoes what f(x) has done
How to find the inverse function
write the function as y =
Interchange the x and y variables
rearrange to make y the subject
What is the domain and range of f-1(x)
the domain of f-1(x) is the range of f(x)
The range of f-1 (x) is the domain of f(x)
What translation of y = f(x) is the graph y = f(x) + a
it is a translation by the vector (0, a)
What translation of y = f(x) is the graph y = f(x + a)
It is a translation by the vector (-a, 0)
what is the graph of y = - f(x) a reflection of
It is a reflection of the graph y = f(x) in the x axis
