Polynomial assignment
What is a variable?
"x" and "y" In this example "x" and "y" are the variables. EX: 2x + y = 5
What is the shape of a quartic function and degree?
A "W" shape 4th degree.
What is a polynomial function?
A polynomial function is a function such as a quadratic, cubic, quartic and so on, involving only non-negative powers of x. EX: f(x)= 2x^3 - 2x^2 - 8x + 8 In this example the line on the graph goes down, up, down, up on the points x = -2, x = 1, x = 2 , y = 4
What is the y - intercept of a polynomial function?
A y - intercept is the point where the function has an input value of zero.
What is the shape of cubic function and the degree?
An "S" shape 3rd degree.
What is a binomial?
Binomials are equation with 2 terms. EX: 5x - 1
What are constants?
Constants are terms at the end of a trinominal. These numbers don't have any variables behind them. In this example "c" is the constant. EX: ax^2 + bx + c= 0
What is the shape of a quintic function and the degree?
Down, up, down, up, down, up 5th degree.
What is the number of turns in a polynomial equation?
It's a part of the graph where the graph changes from increasing to decreasing or decreasing to increasing (rising to falling) (falling to rising). You will take the highest degree and subtract 1 from it. EX: x^4 - 6x^3 + 3x^2 + 10x - 3 degree = 4 the highest degree in this equation is 4, so we will take 4 and subtract it by one which will give us 3 for the turning points. (3 turning points)
What is a monomial?
Monomials are equations with 1 term. EX: 3xy^2
What is a polynomial?
Polynomial means that there are many terms. They can be constants, variables, and exponents. Polynomials can be added, subtracted, multiplied, and divided. EX: 5xy^2 - 3x + 5y^3 - 3
What is the shape of a constant function and the degree?
Side to side 0 degree.
What is the shape of a linear function and the degree?
Slanted 1st degree.
What is end behavior?
The end behavior is the behavior of the graph. This is the f(x) as x approaches positive infinity or negative infinity. The leading coefficient determines the end behaviors of the graph. EX: The lines on the graph will be either a upwards "u" for positive, upside down u for negative, a backwards s for positive or a right-side of a "s" for negative.
How do you find multiplicty?
The number of times a factor becomes factored in a equation EX: The 0 is used with this factor is x = 2 has a multiplicity of 2. This because the factor x - 2 shows up twice
What is multiplicity?
The number of times the given factor appears in factored form. EX: 1, 2, 3
What is a trinomial?
Trinomials are equations with 3 terms. EX: 3x + 5y^2 - 3
What is the shape of a quadratic function and the degree?
U shaped 2nd degree.
What is an exponent?
it's the number that hangs over the variable. Only 0, 1, 2, 3..and so on are examples of good exponents In this example ^2 would be the exponent. EX: -6y^2 2x^3
What is a x - intercept in polynomial function?
x - intercepts happen when the output is 0. You need to factor the polynomial to find the output of 0, then set it to 0. EX: (3, 0) (3, 0) and (-3, 0 ) (-3, 0)
