Quadratic Functions
What is the formula for the vertex's x value?
x=-b/(2a)
What is a power function?
f(x)=ax^n
What is an x int?
The x value where the function intersects the x axis.
What is a y intercept?
The y value where the function intersects the y axis.
What is the domain of
f(x)=x^2+3
(-\infty,\infty)
What is the vertex of
f(x)=x^2-6x+8?
x=3
Identify the degree and leading coefficient of
f(x)=3x^4
Degree is 3, leading coefficient is 4.
Find the x intercepts of
f(x)=x^2-9
x = \pm3
How do you find the y intercept of any function?
Plug in zero to the function and simplify.
What is the domain of
f(x)=1/x
(-\infty,0) \cup (0,\infty)
If the quadratic is concave down, what do we know about the leading coefficient 'a' ?
a is negative.
Identify the degree and leading coefficient of
g(x)=3x-4x^2+1
Degree is 2, leading coefficient is -4.
What do we know about the multiplicity when the function bounces off the x axis?
The x intercept has EVEN multiplicity.
What is the y int of
f(x)=3x^2-2x+5?
(0,5)
What is the domain of
f(x)=\sqrt(x-4)
[4,\infty)
Solve
x^2-5x+6=0
x=2,3
Describe the end behavior of
f(x)=3x^3
x \to \infty, f(x) \to \infty
x \to -\infty, f(x) \to -\infty
Solve for the x intercepts of
g(x)=x^2+4x+4
x=-2
What is the y int of
g(x) = \sqrt(x+4)/(x-1)
(0,-2)
What is the domain of
f(x)=(1)/(x^2-4)
(-\infty,-2)\cup(-2,2)\cup(2,\infty)
Solve
2x^2-x-1=0
x=1,-1/2
What is the end behavior of
f(x)=4x^4+3x^3+2x^2+x+1
x\to \infty, f(x) \to \infty
x\to -\infty, f(x) \to \infty
What is the x intercept of
x=(2x-1)/(3+x)
x=1/2
What is the y int of
h(x)=x\sqrt(x^2-3)+3x-7
(0,-7)
If f(x) is one-to-one and has domain
(-\infty,\infty)
and range
(0,\infty)
what is the domain of
f^-1(x)
(0,\infty)