A2 U7 End Behavior

Front

What is a quartic function?

Back

A quartic function is a polynomial function of degree 4, which can be expressed in the form f(x) = ax^4 + bx^3 + cx^2 + dx + e, where a ≠ 0.

Front

What is the leading term of a polynomial?

Back

The leading term of a polynomial is the term with the highest degree. For example, in the polynomial f(x) = 3x^3 - 6x^5 - 2x^2 - 5, the leading term is -6x^5.

Front

How do you determine the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in f(x) = 2x^4 - 3x^2 - 2x - 4, the degree is 4.

Front

What does it mean for a polynomial to have real and imaginary solutions?

Back

Real solutions are the x-values where the graph intersects the x-axis, while imaginary solutions occur when the graph does not intersect the x-axis. For example, a polynomial can have 1 real and 2 imaginary solutions.

Front

What is end behavior in the context of polynomials?

Back

End behavior describes how the values of a polynomial function behave as x approaches positive or negative infinity.

Front

What is the end behavior of a quartic function as x approaches negative infinity?

Back

For a quartic function with a positive leading coefficient, as x approaches negative infinity, f(x) approaches positive infinity.

Front

What is the significance of the leading coefficient in determining end behavior?

Back

The leading coefficient determines the direction of the graph's ends. If it is positive, the ends go up; if negative, the ends go down.

Front

How can you find the number of real solutions of a polynomial?

Back

You can find the number of real solutions by analyzing the graph of the polynomial or using the discriminant in the case of quadratics.

Front

What is the relationship between the degree of a polynomial and the number of solutions?

Back

A polynomial of degree n can have up to n real solutions, but it may also have complex solutions.

Front

What is a cubic function?

Back

A cubic function is a polynomial function of degree 3, expressed in the form f(x) = ax^3 + bx^2 + cx + d, where a ≠ 0.