Answered

Find the best solutions to your problems with the help of IDNLearn.com. Find in-depth and accurate answers to all your questions from our knowledgeable and dedicated community members.

Determine the direction that this parabola opens:

[tex]\[ y = -4x^2 - 8x - 7 \][/tex]

Click on the correct answer:
- up
- down

Sagot :

GinnyAnsweridn
To determine the direction that the parabola described by the quadratic equation [tex]\( y = -4x^2 - 8x - 7 \)[/tex] opens, we need to analyze the coefficient of the [tex]\( x^2 \)[/tex] term.

1. Identify the quadratic equation form:
A quadratic equation generally is in the form [tex]\( y = ax^2 + bx + c \)[/tex], where:
- [tex]\( a \)[/tex] is the coefficient of [tex]\( x^2 \)[/tex]
- [tex]\( b \)[/tex] is the coefficient of [tex]\( x \)[/tex]
- [tex]\( c \)[/tex] is the constant term

2. Extract the coefficient [tex]\( a \)[/tex]:
In the given equation, [tex]\( y = -4x^2 - 8x - 7 \)[/tex]:
- The coefficient [tex]\( a \)[/tex] is [tex]\( -4 \)[/tex].

3. Determine the direction of the parabola:
- If [tex]\( a > 0 \)[/tex], the parabola opens upwards.
- If [tex]\( a < 0 \)[/tex], the parabola opens downwards.

Since [tex]\( a = -4 \)[/tex], which is less than 0, the parabola opens downwards.

Therefore, the direction that this parabola opens is:

down
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your questions deserve accurate answers. Thank you for visiting IDNLearn.com, and see you again for more solutions.