Quadratics
Polynomials
Functions
Graphs
Rational Expressions
100
Given the quadratic function, find its vertex. The axis of symmetry can be found using x = -b/2a.
f(x) = x2 - 8x + 9
What is (4, -7)?
100
Divide:
(3x^2- 8x + 5) -: (x - 2)
What is
3x - 2 + 1/(x-2)
100
Suppose f(x) = x2 - 4 and g(x) = x + 7. Find f(x) - g(x).
What is x2 - x - 11?
100
State the domain and range of the function:
f(x) = sqrt(x - 1) + 2
What is:
Domain: [1, oo)
Range: [2, oo)
100
Simplify:
(x^2+5x+6)/(x^2-x-12)
What is:
(x+2)/(x-4)
200
How many and what type of solutions does the graph have?
What is 2 real solutions?
200
Use the Rational Root Theorem to list all possible rational zeros of the polynomial
p(x) = 12x4 + 9x3 - 3x2 - 4x + 5
What is
+-(1, 5, 1/2, 1/3, 1/4, 1/6, 1/12, 5/2, 5/3, 5/4, 5/6, 5/12)
200
Given h(x) = x2 + 4 and g(x) = x - 1, find h(x) * g(x).
What is x3 - x2 + 4x - 4?
200
Given the parent function graph of:
f(x) = sqrt x
describe the transformations to the function:
g(x) = sqrt(x-3) + 5
Horizontal shift right 3; Vertical shift up 5.
200
Multiply:
(x^2-4)/(x+3)*(x^2+8x+15)/(x^2+7x+10)
What is x - 2?
300
State the vertex and the x-intercept(s) of the graph below.
What is:
Vertex: (-1, -4)
X-intercepts: (-3, 0) & (1, 0)?
300
Given the zero of 2, find the other zeros for the polynomial
x3 - 2x2 + 3x - 6
+-isqrt3
300
Find f(g(6)) if f(x) = 4x + 1 and g(x) =
sqrt (x - 2)
What is 9?
300
Which equation created the graph shown?
a.
y=1/2(x-2)^2(x+3)
y=-1/2(x-2)(x+3)^2
y=1/2(x+2)(x-3)^2
y=-1/2(x+2)(x-3)^2
What is
y=-1/2(x+2)(x-3)^2
300
Divide:
(x^2+8x+12)/(x+6)-:(x^2-x-6)
What is:
1/(x-3)
400
An object is launched at 17.8 meters per second from a 50.2 meter tall platform. The equation for the object's height h(t) at time t seconds after launch is h(t) = -4.9t2 + 17.8t + 50.2 where h(t) is in meters. What is the height of the object after 3 seconds?
What is 59.5 meters?
400
Find all of the rational zeros of
f(x) = x3 - 3x2 - 4x + 12
What is x = 3, 2, -2?
400
If f(x) = x2 + 3, and g(x) = x - 1, find f(g(x)).
What is x2 - 2x + 4?
400
Graph:
y = (1/3)^x
400
Add:
2/(x+3)+7/(x-1)
What is:
(9x+19)/((x-1)(x+3))
500
Solve: x4 -12x2 - 64 = 0
What is
x = +- 4, x = +-2i
500
Given the following solutions to a polynomial, x = 2, 4, -3, write the function.
What is x3 - 3x2 - 10x + 24?
500
Find the inverse of f(x) = 3x - 5.
What is f^-1(x) = (1/3)x + 5/3
500
Describe the end behavior of the function:
f(x) = -2x4 +3x3 + 5x - 1
Both tails at negative infinity
500
Solve:
x/(x-5)+x=(3x-10)/(x-5)
What is 2?