Answered

Discover a wealth of information and get your questions answered on IDNLearn.com. Discover trustworthy solutions to your questions quickly and accurately with help from our dedicated community of experts.

Question 8 of 10: Parabolas with Vertices at the Origin

The equation below describes a parabola. If [tex]\(a\)[/tex] is positive, which way does the parabola open?

[tex]\[ y = ax^2 \][/tex]

A. Left
B. Up
C. Right
D. Down

Sagot :

GinnyAnsweridn
Alright, let's determine which direction the parabola opens given the equation [tex]\( y = ax^2 \)[/tex].

1. Understanding the Basic Equation:
The given equation [tex]\( y = ax^2 \)[/tex] is a standard form of a parabola. This is a quadratic equation where 'y' is expressed in terms of 'x'.

2. Coefficient 'a' and Its Significance:
- If the coefficient 'a' is positive ([tex]\( a > 0 \)[/tex]), it determines the direction in which the parabola opens.
- In general, for the equation [tex]\( y = ax^2 \)[/tex]:
- When [tex]\( a > 0 \)[/tex] (positive), the parabola opens upwards.
- When [tex]\( a < 0 \)[/tex] (negative), the parabola opens downwards.

3. Answering the Question:
Given that [tex]\( a \)[/tex] is positive, according to the above rules, the parabola will open upwards.

So, the correct option is:
[tex]\[ \text{B. Up} \][/tex]

Therefore, the parabola described by the equation [tex]\( y = ax^2 \)[/tex] opens upwards if [tex]\( a \)[/tex] is positive.
Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Your questions deserve reliable answers. Thanks for visiting IDNLearn.com, and see you again soon for more helpful information.