Variation_End Behavior Test Polynomials Test_Blk 6

Front

What is the standard form of a polynomial?

Back

A polynomial is in standard form when its terms are arranged in descending order of their degree. For example, 9x^3 + 8x^2 - 3x - 11.

Front

What does the leading coefficient of a polynomial indicate?

Back

The leading coefficient indicates the direction of the graph as x approaches positive or negative infinity. A positive leading coefficient with an odd degree means the graph rises to the right and falls to the left.

Front

What does it mean if a polynomial has an odd degree?

Back

An odd degree polynomial will have at least one real root and its end behavior will be opposite on either side of the graph.

Front

What is the significance of the multiplicity of a root?

Back

The multiplicity of a root indicates how many times that root is repeated. An odd multiplicity means the graph crosses the x-axis at that root, while an even multiplicity means it touches the x-axis but does not cross.

Front

How do you determine the end behavior of a polynomial function?

Back

The end behavior can be determined by the leading term of the polynomial. For example, if the leading term is positive and of odd degree, as x approaches +∞, y approaches +∞ and as x approaches -∞, y approaches -∞.

Front

What does it mean if a polynomial crosses the x-axis?

Back

If a polynomial crosses the x-axis at a certain point, it indicates that the corresponding x-value is a root of the polynomial with an odd multiplicity.

Front

What is the difference between even and odd degree polynomials?

Back

Even degree polynomials have the same end behavior on both sides (either both up or both down), while odd degree polynomials have opposite end behavior (one side up and the other down).

Front

How do you identify the roots of a polynomial function?

Back

The roots of a polynomial function can be found by setting the polynomial equal to zero and solving for x. For example, for y = (x + 2)(x - 7)^3, the roots are x = -2 and x = 7 with multiplicity 3.

Front

What is the standard form of the polynomial y = (x + 2)(x - 7)^3?

Back

The standard form is obtained by expanding the polynomial: y = x^4 - 21x^3 + 147x^2 - 294x - 0.

Front

What does the term 'leading term' refer to in a polynomial?

Back

The leading term is the term in a polynomial with the highest degree. It determines the end behavior of the polynomial.