IDNLearn.com connects you with a community of experts ready to answer your questions. Get prompt and accurate answers to your questions from our community of experts who are always ready to help.

Which graph could represent the function [tex]$f(x) = (x + 3.8)^2 - 2.7$[/tex]?

Sagot :

To determine which graph could represent the function [tex]\( f(x) = (x+3.8)^2 - 2.7 \)[/tex], we need to analyze its characteristics. Let's break it down step by step:

### 1. Form of the function:
The given function [tex]\( f(x) = (x+3.8)^2 - 2.7 \)[/tex] is a quadratic function, which can be written in the standard form for a parabola [tex]\( f(x) = a(x - h)^2 + k \)[/tex]. Here:

- [tex]\( a = 1 \)[/tex] (since the coefficient of the squared term is implicitly 1, which is positive),
- [tex]\( h = -3.8 \)[/tex],
- [tex]\( k = -2.7 \)[/tex].

### 2. Vertex of the parabola:
The vertex of the parabola given by [tex]\( f(x) = a(x - h)^2 + k \)[/tex] is at the point [tex]\( (h, k) \)[/tex]. For our function:

- [tex]\( h = -3.8 \)[/tex],
- [tex]\( k = -2.7 \)[/tex].

So, the vertex is [tex]\( (-3.8, -2.7) \)[/tex].

### 3. Direction of the parabola:
Since the coefficient [tex]\( a \)[/tex] of the squared term [tex]\( (x + 3.8)^2 \)[/tex] is positive (i.e., [tex]\( a = 1 \)[/tex]), the parabola opens upwards.

### 4. Overall shape and properties:
Summarizing the given function:
- The vertex of the parabola is at [tex]\( (-3.8, -2.7) \)[/tex].
- The parabola opens upwards.

Given these properties, we can confidently state that the graph representing the function [tex]\( f(x) = (x+3.8)^2 - 2.7 \)[/tex] is a parabola with its vertex located at the point [tex]\((-3.8, -2.7)\)[/tex] and it opens upwards. This defines the specific shape and location of the parabola on the coordinate plane.