Quadratics
What is standard form?
f(x) = ax^2 +bx +c
Absolute value gives the _____ between two numbers.
distance
What is a condition in order to find the inverse function?
Must be 1-1
How to find points:
g(x) = f(x) +c
add c to y-values
What is vertex form?
f(x) = a(x-h)^2 +k
Solve |2x+1| - 6 =0
x=-7/2, 5/2
What is the inverse of f(x) = x^3
cubed root of x
How to find points:
g(x) = f(x-c)
add c to x-values
How to find vertex?
h= -b/2a
k = f(h)
Solve 2 = 3|x-1| -9
x=14/3, -8/3
Outline the steps for finding inverse
solve for x
switch x and y
set y = f inverse
What is the transformation:
g(x) = -cf(x)
c>1
Vertical stretch by c units, reflection over x-axis
Find the vertex form of the following:
f(x) = 2x^2 +4x + 2
f(x) = 2(x+1)^2
Solve 1 = |x+1| + 8
No solution
The inverse of a function is that function reflected over _____
y=x
Describe the transformation on g(x) = -2^x +1
reflection over x
up 1
Find the x and y-intercepts:
f(x) = 2x^2 +16x+30
x=-5,-3
y=30
Solve |1-2x| < 6
(-5/2, 7/2)
Why would we restrict a function to find the inverse?
If our function is not one to one, the inverse will not be a function.
Describe the transformation and graph
stretch by 3 units
down 1
horizontal shift left units
reflection over y