Polynomials

Front

Degree classification of the polynomial x²+4x-8.

Back

quadratic

Answer explanation

The polynomial x² + 4x - 8 has a degree of 2, which classifies it as a quadratic polynomial. Quadratic polynomials are defined as those with the highest exponent of 2.

Front

What is the degree of the polynomial f(x) = 3x² + 4x - 5?

Back

Degree 2 (quadratic)

Answer explanation

The degree of a polynomial is determined by the highest power of its variable. In f(x) = 3x² + 4x - 5, the highest power is 2 (from 3x²), so the degree is 2 (quadratic).

Front

End behavior of f(x) = 2x^3 - x + 5 as x → ±∞?

Back

Left down Right up

Answer explanation

The polynomial f(x) = 2x^3 - x + 5 has a degree of 3 (odd) and a positive leading coefficient (2). Therefore, as x approaches negative infinity, f(x) goes to negative infinity (left down), and as x approaches positive infinity, f(x) goes to positive infinity (right up).

Front

Determine the end behavior of the ramp modeled by the function f(x) = -2x² + 3x.

Back

Left down   Right down

Answer explanation

The leading coefficient of f(x) = -2x² + 3x is negative, and the degree is 2 (even). This means both ends of the graph will go down. Therefore, the end behavior is Left down & Right down.

Front

Priya is analyzing the graph of a function to determine the type of symmetry. Based on the graph shown, the function is:

Back

odd

Answer explanation

The function is odd because it satisfies the condition f(-x) = -f(x) for all x in its domain. This means the graph is symmetric about the origin, confirming it is an odd function.

Front

How many different values of x (zeros) will make the total arrangements zero for the polynomial function P(x) = 3x⁴+4x-8?

Back

4

Answer explanation

The polynomial P(x) = 3x^4 + 4x - 8 is a degree 4 polynomial, which means it can have up to 4 zeros. By the Fundamental Theorem of Algebra, it has exactly 4 zeros, counting multiplicities. Thus, the correct answer is 4.

Front

Factored form of function with zeros at 2, 3, and -1.

Back

(x-2)(x-3)(x+1)

Answer explanation

The zeros of the function are 2, 3, and -1. In factored form, each zero corresponds to a factor of the form (x - zero). Thus, the correct factors are (x-2), (x-3), and (x+1), leading to the answer (x-2)(x-3)(x+1).

Front

In the above graph complete the following end behavior: (f(x)=y)
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____

Back

+∞
+∞

Answer explanation

The graph shows that as x approaches -∞, f(x) approaches +∞, and as x approaches +∞, f(x) also approaches +∞. Therefore, the correct end behavior is +∞ for both cases.

Front

Zoe is tracking the elevation of a roller coaster over time, and the graph above shows how the elevation changes as the ride progresses. Complete the following end behavior for the roller coaster's elevation:
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____

Back

-∞
-∞

Answer explanation

The graph's end behavior shows that as x approaches -∞, f(x) also approaches -∞, and as x approaches +∞, f(x) continues to approach -∞. Thus, the correct choice is -∞ for both ends.

Front

Back

y = -(x - 2)(x + 1)²