Graphing Polynomials: Solutions and End Behavior

The video tutorial covers unit 7 day 3 homework for Algebra 2 students, focusing on the fundamental theorem of algebra. It explains the zero product property and its application in solving equations. The tutorial also demonstrates graphing techniques, including understanding the behavior of graphs and plotting solutions. Advanced problem-solving methods are discussed, emphasizing factoring and the use of calculators for square roots.

What is the degree of a polynomial and how does it relate to the number of solutions?

• The degree is the coefficient of the highest term and it determines the number of solutions.

• The degree is the sum of the exponents and it determines the number of solutions.

• The degree is the number of terms and it determines the number of solutions.

• The degree is the highest exponent and it determines the number of solutions.

When graphing a polynomial function, what is the first step after obtaining the factors?

• Determine the end behavior.

• Set each factor equal to zero.

• Plot the y-intercept.

• Find the vertex of the graph.

What does the zero product property state?

• If a product of factors is zero, all factors must be zero.

• If a product of factors is zero, the difference of the factors must be zero.

• If a product of factors is zero, at least one of the factors must be zero.

• If a product of factors is zero, the sum of the factors must be zero.

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

• By looking at the leading coefficient and the degree of the polynomial.

• By calculating the roots of the polynomial.

• By finding the y-intercept.

• By determining the number of terms in the polynomial.

What is the approximate value of the square root of 5?

• 3.0

• 1.5

• 2.2

• 2.5

What is the first step in solving a polynomial equation by factoring?

• Set the equation to zero.

• Find the y-intercept.

• Factor out the greatest common factor (GCF).

• Determine the degree of the polynomial.

What does GCF stand for in polynomial factoring?

• Greatest Coefficient Function

• Greatest Common Function

• Greatest Coefficient Factor

• Greatest Common Factor

How do you solve a polynomial equation after factoring out the GCF?

• Set each factor equal to zero and solve for the variable.

• Plot the graph and solve for the variable.

• Find the y-intercept and solve for the variable.

• Determine the degree and solve for the variable.

What should you do if a polynomial equation has no GCF?

• Set the equation to zero and solve directly.

• Use the quadratic formula.

• Factor the polynomial using other methods.

• Graph the polynomial to find the solutions.

What is the end behavior of an even positive polynomial function?

• It goes down on both sides.

• It goes down on the left and up on the right.

• It goes up on both sides.

• It goes up on the left and down on the right.