Questions: Complete parts (a) and (b) for f(x)=-7+x-2x^2. (a)State the degree and leading coefficient of f. (b)State the end behavior of the graph of f. (a) The degree of f is 2 and its leading coefficient is -2. (Type whole numbers.) (b) Choose the correct answer below. A. The graph of f falls to the left and rises to the right. B. The graph of f rises to the left and falls to the right. C. The graph of f falls both to the left and to the right. D. The graph of f rises both to the left and to the right.

Solution Steps

To solve part (a), identify the degree and leading coefficient of the polynomial function \( f(x) = -7 + x - 2x^2 \). The degree is the highest power of \( x \) in the polynomial, and the leading coefficient is the coefficient of that term. For part (b), determine the end behavior of the graph based on the degree and leading coefficient. Since the degree is even and the leading coefficient is negative, the graph will fall to both the left and the right.

The function is given by \( f(x) = -2x^2 + x - 7 \). The degree of the polynomial is the highest power of \( x \), which is \( 2 \). The leading coefficient is the coefficient of the term with the highest degree, which is \( -2 \).

Since the degree of the polynomial is even (\( 2 \)) and the leading coefficient is negative (\( -2 \)), the end behavior of the graph of \( f \) is that it falls both to the left and to the right.

Final Answer