Quadratics, Functions, Transformations, Geometry Flashcards
What is an quadratic equation
In the form ax2+bx+c=y
What is a discriminant
b2-4ac determining root nature
State the 3 root natures
b2-4ac=0 real and equal
b2-4ac>0 real and different
b2-4ac<0 no roots
What is a function?
Rule that maps a single number to another single number
What are domain and range?
Inputs for a function is domain
Set of outputs is range
A function is inverse only if…
It is one one
What is a one-one function
Distinct inputs have distinct outputs
State the two opposite domain / range rules for f(x)
Domain of f = range of f-1
Domain of f-1= range of f
How is graph of f-1(x) in relation to f(x)
F(x) is reflected in y=x
f(x+a) is _ of _
Horizontal translation of -a
f(x)+a
Vertical translation of +a
f(ax) is _ of _ : _
Horizontal stretch of scale factor:1/a
multiply x coordinate by 1/a
af(x) is _ of :
Vertical stretch of scale factor:a
multiply y coordinate by a
What is gradient?
Measure of a straight lines slope with respect to it’s X axis
State formula of gradient
(y2-y1/x2-x1)
Formula of length a line joining 2 points
√(x1-x2)^2 + (y1-y2)^2
State the rules of gradient for parallel and perpendicular lines
Para: equal
Perpen: product=-1
Midpoint formula:
(x1+x2/2 , y1+y2/2)
Equation of a line:
Y=mx+c
Equation of a line with gradient m and passing through (x1, y1)
(y-y1) = m(x-x1)
Equation of a line passing through 2 points
(y-y1) = (y2-y1/x2-x1)(x-x1)
Equation of a circle with centre (a, b) and radius r
(x-a)^2 + (y-b)^2 = r^2
x^2+y^2+2gx+2fy+c=0 represents?
A circle
Centre: (-g, -f) (that is /2)
Radius: √ g^2 + f^2 -c
