Answered

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2. If the value of [tex]a[/tex] in the quadratic function [tex]f(x)=ax^2+bx+c[/tex] is -8, the function will

A. open up and have a maximum
B. open down and have a minimum
C. open up and have a minimum
D. open down and have a maximum

Sagot :

GinnyAnswer
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.
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