Question

quadratic function
$f(x) = ax^2 + bx + c$, where $a \
eq 0$

Explanation:

To determine the parts of the quadratic function \( f(x) = ax^2 + bx + c \) (where \( a
eq 0 \)):

Step 1: Identify the coefficient of \( x^2 \)

The term \( ax^2 \) has \( a \) as the coefficient of \( x^2 \). In the standard form of a quadratic function, \( a \) is the leading coefficient (and \( a
eq 0 \) to ensure it is quadratic).

Step 2: Identify the coefficient of \( x \)

The term \( bx \) has \( b \) as the coefficient of \( x \). This is the linear coefficient.

Step 3: Identify the constant term

The term \( c \) is the constant term (it has no variable attached).

If the question is to label the blanks (from left to right under the formula):

• First blank (under \( ax^2 \)): \( \boldsymbol{a} \) (leading coefficient, coefficient of \( x^2 \))
• Second blank (under \( bx \)): \( \boldsymbol{b} \) (coefficient of \( x \))
• Third blank (under \( c \)): \( \boldsymbol{c} \) (constant term)

For example, if the blanks are to be filled with the names/roles:

• First: "Leading coefficient (coefficient of \( x^2 \))"
• Second: "Coefficient of \( x \) (linear term coefficient)"
• Third: "Constant term"

If you need to confirm the parts of the quadratic function, the three components are:

• \( a \): Coefficient of \( x^2 \) (leading coefficient, \( a

eq 0 \))

• \( b \): Coefficient of \( x \) (linear coefficient)
• \( c \): Constant term

Final Answer (if filling the blanks with \( a \), \( b \), \( c \) in order):

From left to right: \( \boldsymbol{a} \), \( \boldsymbol{b} \), \( \boldsymbol{c} \)

Answer:

To determine the parts of the quadratic function \( f(x) = ax^2 + bx + c \) (where \( a
eq 0 \)):

Step 1: Identify the coefficient of \( x^2 \)

The term \( ax^2 \) has \( a \) as the coefficient of \( x^2 \). In the standard form of a quadratic function, \( a \) is the leading coefficient (and \( a
eq 0 \) to ensure it is quadratic).

Step 2: Identify the coefficient of \( x \)

The term \( bx \) has \( b \) as the coefficient of \( x \). This is the linear coefficient.

Step 3: Identify the constant term

The term \( c \) is the constant term (it has no variable attached).

If the question is to label the blanks (from left to right under the formula):

• First blank (under \( ax^2 \)): \( \boldsymbol{a} \) (leading coefficient, coefficient of \( x^2 \))
• Second blank (under \( bx \)): \( \boldsymbol{b} \) (coefficient of \( x \))
• Third blank (under \( c \)): \( \boldsymbol{c} \) (constant term)

For example, if the blanks are to be filled with the names/roles:

• First: "Leading coefficient (coefficient of \( x^2 \))"
• Second: "Coefficient of \( x \) (linear term coefficient)"
• Third: "Constant term"

If you need to confirm the parts of the quadratic function, the three components are:

• \( a \): Coefficient of \( x^2 \) (leading coefficient, \( a

eq 0 \))

• \( b \): Coefficient of \( x \) (linear coefficient)
• \( c \): Constant term

Final Answer (if filling the blanks with \( a \), \( b \), \( c \) in order):

From left to right: \( \boldsymbol{a} \), \( \boldsymbol{b} \), \( \boldsymbol{c} \)