Question
Identify the following key attributes of the polynomial
f(x)= – 4x2 + 9
Does the function have a maximum or minimum?
Group of answer choices
maximum
minimum
f(x)= – 4x2 + 9
Does the function have a maximum or minimum?
Group of answer choices
maximum
minimum
Answers
GPT-4o mini
To identify whether the polynomial \( f(x) = -4x^2 + 9 \) has a maximum or minimum, we need to look at the coefficient of the \( x^2 \) term.
1. The leading coefficient (the coefficient of \( x^2 \)) is -4, which is negative.
2. For a quadratic function of the form \( ax^2 + bx + c \):
- If \( a > 0 \), the parabola opens upwards, and the function has a minimum.
- If \( a < 0 \), the parabola opens downwards, and the function has a maximum.
Since the leading coefficient is negative (specifically \( -4 < 0 \)), this means the function has a maximum.
Therefore, the answer is:
**maximum**.
1. The leading coefficient (the coefficient of \( x^2 \)) is -4, which is negative.
2. For a quadratic function of the form \( ax^2 + bx + c \):
- If \( a > 0 \), the parabola opens upwards, and the function has a minimum.
- If \( a < 0 \), the parabola opens downwards, and the function has a maximum.
Since the leading coefficient is negative (specifically \( -4 < 0 \)), this means the function has a maximum.
Therefore, the answer is:
**maximum**.