Answered

IDNLearn.com provides a seamless experience for finding the answers you need. Find the solutions you need quickly and accurately with help from our knowledgeable community.

Question 2

A parabola with the equation [tex]\( y = a(x - b)^2 + c \)[/tex] has a minimum point.

Part A

What are the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex]?

Select the three that apply.

A. [tex]\( a = -1 \)[/tex]

B. [tex]\( a = 1 \)[/tex]

C. [tex]\( b = 2 \)[/tex]

D. [tex]\( b = -2 \)[/tex]

Sagot :

GinnyAnsweridn
Alright, let's break down the problem step by step to determine the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] for the given parabolic equation [tex]\( y = a(x-b)^2 + c \)[/tex]:

1. Understanding 'a':
- The coefficient [tex]\(a\)[/tex] determines the direction the parabola opens. If [tex]\(a\)[/tex] is positive, the parabola opens upwards, indicating a minimum point. If [tex]\(a\)[/tex] is negative, the parabola opens downwards, indicating a maximum point.
- Since the question states that the parabola has a minimum plane, [tex]\(a\)[/tex] must be positive.
- Therefore, the possible value for [tex]\(a\)[/tex] is [tex]\(a = 1\)[/tex].

2. Understanding 'b':
- The parameter [tex]\(b\)[/tex] indicates the horizontal shift of the parabola. It does not affect whether the parabola has a minimum or maximum, only its position along the x-axis.
- The question provides two possible values for [tex]\(b\)[/tex]: [tex]\(b = 2\)[/tex] and [tex]\(b = -2\)[/tex].
- Both values are valid and do not violate any conditions of the problem.

3. Understanding 'c':
- The coefficient [tex]\(c\)[/tex] indicates the vertical shift of the parabola. Like [tex]\(b\)[/tex], it does not affect the direction in which the parabola opens, it only shifts the parabola up or down on the y-axis.
- The problem does not provide specific values for [tex]\(c\)[/tex], but it can be any real number since it simply moves the parabola vertically without changing its shape or the direction it opens.

Summing up, the correct values are:
- [tex]\(a = 1\)[/tex] (because the parabola opens upwards to have a minimum)
- [tex]\(b = 2\)[/tex] and [tex]\(b = -2\)[/tex] (either value is acceptable as it only represents a horizontal shift)

For [tex]\(c\)[/tex], it can take any real value, but since this question only allows selection from the given choices of [tex]\(a\)[/tex] and [tex]\(b\)[/tex], it is not directly mentioned but implied.

Therefore, the selections you should make are:
- [tex]\(a = 1\)[/tex]
- [tex]\(b = 2\)[/tex]
- [tex]\(b = -2\)[/tex]
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. IDNLearn.com is dedicated to providing accurate answers. Thank you for visiting, and see you next time for more solutions.