TAKE HOME!! *AA C&C FLASHCARD: Graphs of Polynomials (Parts 1-3)

The End Behavior of a polynomial function describes how the function behaves as the input (x) approaches positive or negative infinity. It is determined by the leading term of the polynomial.

As @@x ightarrow ext{infinity}, f(x) ightarrow - ext{infinity} $$and as$$ x ightarrow - ext{infinity}, f(x) ightarrow - ext{infinity}@@.

The End Behavior will be such that as @@x ightarrow ext{infinity}, f(x) ightarrow - ext{infinity} $$and as$$ x ightarrow - ext{infinity}, f(x) ightarrow - ext{infinity}@@.

A zero of a polynomial is a value of $$x$$ for which the polynomial evaluates to zero, meaning the graph of the polynomial intersects the x-axis.

Set each factor equal to zero: 1) $$3x = 0$$ gives $$x = 0$$ ; 2) $$x + 2 = 0$$ gives $$x = -2$$ ; 3) $$2x + 7 = 0$$ gives $$x = -\frac{7}{2}$$ .

The leading coefficient determines the direction of the End Behavior of the polynomial function. If it is positive, the function will rise to infinity on the right; if negative, it will fall to infinity on the right.

A polynomial function is expressed as $$f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0$$ , where $$a_n$$ is the leading coefficient and $$n$$ is the degree of the polynomial.

A polynomial of degree 4 can have up to 4 real zeros and its graph can have up to 3 turning points.

The degree of a polynomial is the highest power of the variable $$x$$ in the polynomial expression.

A polynomial of degree $$n$$ can have at most $$n$$ real zeros, counting multiplicities.