Answered

Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

The graph of [tex]\( f(x) = 6(x - 6)^2 - 3 \)[/tex] is a parabola that opens [up/down], with its vertex at [tex]\( (x, y) = ( \_\_ , \_\_ ) \)[/tex], and [tex]\( f(6) = \_\_ \)[/tex] is the [minimum/maximum] value of [tex]\( f \)[/tex].

Sagot :

GinnyAnswer
Let's break down the solution step-by-step for the given function [tex]\( f(x) = 6(x - 6)^2 - 3 \)[/tex].

1. Identify the Vertex Form of the Quadratic Function:

The given function is in the form [tex]\( f(x) = a(x - h)^2 + k \)[/tex], where [tex]\( (h, k) \)[/tex] represents the vertex of the parabola.

2. Determine the Coefficient [tex]\(a\)[/tex]:

Here, the coefficient [tex]\( a \)[/tex] is 6, which is positive, indicating that the parabola opens upwards.

- Answer: The parabola opens upwards.

3. Find the Vertex [tex]\((h, k)\)[/tex]:

Compare the given function [tex]\( f(x) = 6(x - 6)^2 - 3 \)[/tex] with the standard form [tex]\( f(x) = a(x - h)^2 + k \)[/tex].

- We see that [tex]\( h = 6 \)[/tex] and [tex]\( k = -3 \)[/tex].

- Therefore, the vertex of the parabola is at [tex]\( (x, y) = (6, -3) \)[/tex].

4. Calculate [tex]\( f(6) \)[/tex]:

To find the value of the function at [tex]\( x = 6 \)[/tex]:

[tex]\( f(6) = 6(6 - 6)^2 - 3 \)[/tex]

Simplify inside the parentheses first:

[tex]\( 6 - 6 = 0 \)[/tex]

Then square the result:

[tex]\( 0^2 = 0 \)[/tex]

Multiply by 6:

[tex]\( 6 \times 0 = 0 \)[/tex]

Finally, subtract 3:

[tex]\( 0 - 3 = -3 \)[/tex]

- Therefore, [tex]\( f(6) = -3 \)[/tex].

5. Compile the Results:

- The vertex of the parabola is at [tex]\( (6, -3) \)[/tex].
- The value of the function at [tex]\( x = 6 \)[/tex] is [tex]\( -3 \)[/tex].

Putting this all together in the final blanks:
- The graph of [tex]\( f(x) = 6(x - 6)^2 - 3 \)[/tex] is a parabola that opens upwards, with its vertex at [tex]\( (x, y) = (6, -3) \)[/tex], and [tex]\( f(6) = -3 \)[/tex] is the minimum value of [tex]\( f \)[/tex].
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.