Understanding Polynomial Functions

This video tutorial explores the zeros, factors, and graphs of polynomial functions. It begins with an introduction to polynomial functions and their properties, including real rational zeros and their relationship to factors and graphs. The tutorial then provides three examples: a degree four polynomial, a degree three polynomial, and a polynomial equation. Each example demonstrates how to find x-intercepts, write polynomials in factored form, and verify solutions using graphs. The video emphasizes the importance of multiplicity in determining the behavior of polynomial graphs at x-intercepts.

What is the relationship between a zero of a polynomial and its graph?

• A zero is a point where the graph crosses the y-axis.

• A zero is a point where the graph is tangent to the x-axis.

• A zero is a point where the graph touches the y-axis.

• A zero is a point where the graph crosses the x-axis.

In a polynomial function, what does a zero with multiplicity two indicate about the graph?

• The graph has a vertical asymptote at that point.

• The graph touches the x-axis and turns around at that point.

• The graph has a horizontal asymptote at that point.

• The graph crosses the x-axis at that point.

Tags

CCSS.HSF-IF.C.7C

How many x-intercepts does a degree four polynomial with zeros at x=0, x=3, and x=-1 have?

• One

• Four

• Two

• Three

What happens to the graph of a polynomial at a zero with odd multiplicity?

• The graph touches the x-axis and turns around.

• The graph crosses the x-axis.

• The graph has a vertical asymptote.

• The graph has a horizontal asymptote.

For a degree three polynomial, if the graph crosses the x-axis at x=-2, what is the multiplicity of this zero?

• One

• Two

• Three

• Four

If a polynomial has a zero at x=1 with multiplicity two, what does this imply about the graph at x=1?

• The graph crosses the x-axis at x=1.

• The graph has a vertical asymptote at x=1.

• The graph touches the x-axis and turns around at x=1.

• The graph has a horizontal asymptote at x=1.

What is the leading coefficient of a polynomial if it is given as -0.5(x+2)(x-1)^2?

• 1

• -1

• 0.5

• -0.5

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CCSS.HSA.APR.B.3

In verifying solutions of a polynomial equation, what are the x-intercepts used for?

• To determine the degree of the polynomial.

• To find the y-intercepts.

• To find the leading coefficient.

• To verify the solutions of the equation.

Tags

CCSS.HSF-IF.C.7C

What are the zeros of the polynomial function 0.25x(x-1)(x-3)(x+4)(x+2)^2?

• x=-1, x=3, x=-4, x=2

• x=-1, x=-3, x=4, x=2

• x=1, x=3, x=4, x=2

• x=1, x=3, x=-4, x=-2

Tags

CCSS.HSF-IF.C.7C

How many x-intercepts does the polynomial 0.25x(x-1)(x-3)(x+4)(x+2)^2 have?

• Two

• Five

• Three

• Four

Tags

CCSS.HSF-IF.C.7C