Bellshaffonidn
Answered

Get detailed and accurate responses to your questions on IDNLearn.com. Our Q&A platform offers detailed and trustworthy answers to ensure you have the information you need.

### Completing the Square to Write in Vertex Form

Write [tex]\( h(x) = x^2 - 6x + 3 \)[/tex] in vertex form by following these steps:

Step 1: Model [tex]\( x^2 - 6x + 3 \)[/tex] by placing tiles in the Product section. First, place the [tex]\( x^2 \)[/tex] and [tex]\( -x \)[/tex] tiles along the left and top borders to form two sides of a square. Then place the [tex]\( + \)[/tex] tiles along the ends of the [tex]\( -x \)[/tex] tiles.

Step 2: Form a square of tiles in the Product section. Add as many zero-pair tiles as necessary. Move the extra [tex]\( - \)[/tex] tiles off to the side.

Sagot :

GinnyAnsweridn
To write the function [tex]\( h(x) = x^2 - 6x + 3 \)[/tex] in vertex form, we use the method of completing the square. Here's a detailed, step-by-step approach:

### Step 1: Understand the Initial Function
We start with the quadratic function:
[tex]\[ h(x) = x^2 - 6x + 3 \][/tex]

### Step 2: Arrange the Terms for Completing the Square
To complete the square, we look at the quadratic and linear terms, [tex]\( x^2 - 6x \)[/tex].

### Step 3: Halve the Coefficient of [tex]\( x \)[/tex] and Square It
Take half the coefficient of [tex]\( x \)[/tex], which is [tex]\(-6\)[/tex]. Halving it gives [tex]\(-3\)[/tex]. Squaring [tex]\(-3\)[/tex] gives:
[tex]\[ (-3)^2 = 9 \][/tex]

### Step 4: Add and Subtract This Square
Add and subtract this square inside the function:
[tex]\[ h(x) = x^2 - 6x + 9 - 9 + 3 \][/tex]

### Step 5: Group to Form a Perfect Square
Combine the first three terms to form a perfect square:
[tex]\[ h(x) = (x - 3)^2 - 9 + 3 \][/tex]

### Step 6: Simplify
Simplify the constant terms:
[tex]\[ h(x) = (x - 3)^2 - 6 \][/tex]

### Final Form in Vertex Form
The vertex form of [tex]\( h(x) = x^2 - 6x + 3 \)[/tex] is thus:
[tex]\[ h(x) = (x - 3)^2 - 6 \][/tex]

### Verification
To verify, you can expand the vertex form to see if it matches the original function:
[tex]\[ (x - 3)^2 - 6 = x^2 - 6x + 9 - 6 = x^2 - 6x + 3 \][/tex]

Thus, the vertex form of the given quadratic function is:
[tex]\[ h(x) = (x - 3)^2 - 6 \][/tex]

This shows the correct transformation using the completing the square method.
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Find clear and concise answers at IDNLearn.com. Thanks for stopping by, and come back for more dependable solutions.