Write the long-run behavior of f(x)=x^6 using arrow notation
As x-->inf, f(x)-->inf
As x-->-inf, f(x)-->inf
100
Find the value that completes the square and then re-write as a perfect square:
y^2 - y + ____
1/4; (y-1/2)^2
100
What is the quadratic formula?
x = -b +- sqrt(b^2 - 4ac)
2a
200
Factor: 4uv + 14u^2 + 12v + 42u
2(u+3)(2v+7u)
200
If a graph has 3 x-intercepts, 4 extrema, and a negative leading coefficient, what is the least possible degree of the polynomial? Sketch a graph that fits these criteria.
degree 5 (nth degree for n-1 extrema)
graphs may vary
200
Solve the following quadratic equation by factoring:
5x^2 - 13x = 28
x = -1
x = -5
200
Sketch the graph of
f(x)=x^2-2x
parabola opens up with x-int at 0 and 2, y-int at 0
300
Factor:
49x^2 + 14x +1
(7x+1)^2
300
What is a polynomial? Define in your own words. Describe the function and the graph.
A sum of terms where the powers on the variable are all positive integers. The graph can be drawn with smooth curves without lifting a pencil, so there are no sharp corners or gaps. Standard form of the equation: f(x)=a+bx+cx^2+dx^3+...+ex^n
300
Use completing the square to find the vertex of
f(x)=-x^2+8x-15
(4,1)
300
Use the Zero Product Property to solve the following quadratic equation.
15x^2 - 29x -14 = 0
(x-4)(5x+7)=0
x = 4
x = -7/5
400
Factor:
3x^5 - 48xy^4
3x(x^2+4y^2)(x+2y)(x-2y)
400
Given f(x)= -3x^3 + 6x^2 + 24x, find the intercepts and long-run behavior. Then graph the polynomial
x-int: (0,0), (-2,0), (4,0)
y-int: (0,0)
As x-->inf, f(x)-->-inf
As x-->-inf, f(x)-->+inf
400
Find the vertex of
f(x)=5x^2+2x-2
(-1/5,-11/5)
400
Solve using the quadratic formula:
2x^2 + 9x + 4 = 0
x = -1/2
x = -4
500
Factor:
125x^3 - 216
(5x-6)(25x^2+30x+36)
500
Write an equation for a polynomial that is degree 5, roots of multiplicity 2 at x=3 and x=1, root of multiplicity 1 at x=-3, and y-intercept at (0,9). Then graph the polynomial.