Factoring
Quadratics
Polynomial Functions
Vocabulary
Factoring and Solving Polynomials
100
The zeros of: y = x^2 + 8x + 15
What are x=-3 and x=-5 ?
100
What is the equation for finding the axis of symmetry?
x=-b/(2a)
100
What is the degree and leading coefficient for the polynomial below?
2x^3+3x^6+2x^4+1x^7
degree = 7
leading coefficient = 1
100
The vertical line that cuts through the center of a parabola.
What is the axis of symmetry?
100
Factor
x^3 - 125
(x-5)(x^2+5x+25)
200
The solutions of: y = x^2 - 11x + 24
What are x=3 and x=8 ?
200
The vertex of:
y = x^2 + 6x +9
What is (-3, 0)
200
Determine if the following are polynomials:
a.
2 + 2/(3*x^2)
b.
2 +2/(3)x^2
c.
sqrt(x) + 6
no, yes, no
200
DOUBLE
A polynomial with the highest degree of 2.
What is a quadratic?
200
Factor
x^3-4x^2+25x-100
(x^2+25)(x-4)
300
The zeros of: y = 2x^2 + x - 15
x = 2.5, -3
300
Graph
y = x^2 +4x +4
What is y = x^2 ?
300
DOUBLE
Graph
f(x) = x^3 - 5x + 6
300
The graph of a quadratic function.
What is a parabola?
300
DOUBLE
Solve by factoring
x^4 +2x^3 +48x^2+96x=0
x = -2, 0, +-4isqrt3
400
The solutions to: y = 5x^2 + 11x +2
What are x=-2 and x=-1/5 ?
400
DOUBLE
Complete the square to solve.
x^2 +12x = 15
x = -6 +-sqrt51
400
Simplify
(3x^3 +6x^2 -x +5) - (2x^3 -4x^2 +7x -15)
x^3+10x^2-8x+20
400
What is another name for the y-intercept? (hint: what do you call the number not being multiplied by a variable in standard form?)
What are the y-intercept and the starting value/constant?
400
Solve
x^4+6x^2-72=0
x = +-2isqrt3, +-sqrt6
500
The solutions of: y = 4x^2 - 36
What are x=3 and x=-3 ?
500
An arrow is launched upwards. The height of the arrow, in meters, after t seconds can be modeled by the function below. After how many seconds will the arrow first reach and altitude of 50 meters? Round to the nearest tenth of a second.
h(t) = -4.9t^2 +120t +4
x ~.39 seconds
500
Find the quotient of
(24x^7y^5 +15x^9y^4-9x^2y^2)/(3x^2y)
8x^5y^4+5x^7y^3-3y
500
Four terms used to describe where a parabola crosses the x-axis.
What are: zeros, solutions, roots, and x-intercepts?
500
If (x - 4) is a factor of the polynomial below, find the remaining factors.
x^3-12x-16
x^2 +4x +4 or (x+2)(x+2)