Question

consider the quadratic function.\\(f(p) = p^2 - 8p - 5\\)\
what are the values of the coefficients and the constant in the function?\
\\(a = -1, b = -8, c = -5\\)\
\\(a = 1, b = -8, c = -5\\)\
\\(a = -1, b = -5, c = 8\\)

Explanation:

Step1: Recall quadratic form

The standard form of a quadratic function is \( f(x) = ax^2 + bx + c \), where \( a \) is the coefficient of \( x^2 \), \( b \) is the coefficient of \( x \), and \( c \) is the constant term.

Step2: Identify coefficients/constant

For \( f(p) = p^2 - 8p - 5 \), compare with \( ax^2 + bx + c \):

• Coefficient of \( p^2 \) (\( a \)): The term \( p^2 \) has a coefficient of \( 1 \) (since \( p^2 = 1 \cdot p^2 \)).
• Coefficient of \( p \) (\( b \)): The term \( -8p \) has a coefficient of \( -8 \).
• Constant term (\( c \)): The term \( -5 \) is the constant, so \( c = -5 \).

Answer:

\( a = 1, b = -8, c = -5 \) (the second option: \( a = 1, b = -8, c = -5 \))