Answer :
Given the quadratic function [tex]\( f(x) = ax^2 + bx + c \)[/tex], let's analyze the behavior of the function based on the value of [tex]\( a \)[/tex].
We know that the quadratic function [tex]\( f(x) = ax^2 + bx + c \)[/tex] can open either upwards or downwards depending on the value of the coefficient [tex]\( a \)[/tex]:
1. If [tex]\( a > 0 \)[/tex], the parabola opens upwards and has a minimum value.
2. If [tex]\( a < 0 \)[/tex], the parabola opens downwards and has a maximum value.
In this problem, it is given that [tex]\( a = -8 \)[/tex]. Since [tex]\( a = -8 \)[/tex] is less than zero ([tex]\( a < 0 \)[/tex]), we can conclude the following about the quadratic function:
- The parabola opens downwards.
- Since it opens downwards, the function will have a maximum value.
Therefore, the correct answer is:
open down and have a maximum.
We know that the quadratic function [tex]\( f(x) = ax^2 + bx + c \)[/tex] can open either upwards or downwards depending on the value of the coefficient [tex]\( a \)[/tex]:
1. If [tex]\( a > 0 \)[/tex], the parabola opens upwards and has a minimum value.
2. If [tex]\( a < 0 \)[/tex], the parabola opens downwards and has a maximum value.
In this problem, it is given that [tex]\( a = -8 \)[/tex]. Since [tex]\( a = -8 \)[/tex] is less than zero ([tex]\( a < 0 \)[/tex]), we can conclude the following about the quadratic function:
- The parabola opens downwards.
- Since it opens downwards, the function will have a maximum value.
Therefore, the correct answer is:
open down and have a maximum.
