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graph the given function by writing it in the standard form \\(y = a(x …

Question

graph the given function by writing it in the standard form \\(y = a(x - h)^2 + k\\) and then using transformations on \\(y = x^2\\). find the vertex, the axis of symmetry, and the x- and y-intercepts.

\\(y = 4x - 11 - x^2\\)

rewrite \\(y = 4x - 11 - x^2\\) in standard form.

\\(y = -(x - 2)^2 - 7\\)
(type an equation. use integers or fractions for any numbers in the equation.)

what kind(s) of transformation(s) occur between the graph of the given function and the graph of \\(y = x^2\\)?
select all that apply.

a. a horizontal shift
b. a reflection across the y-axis
c. a reflection across the x-axis
d. a vertical shift

Explanation:

Rewrite in standard form

Using the Completing the Square and Vertex Form of a Quadratic knowledge points

$$ LATEXBLOCK0 $$

Identify graph transformations

Using the Graph Transformations knowledge point

$$ LATEXBLOCK1 $$

Answer:

Question 1

Rewrite \(y = 4x - 11 - x^2\) in standard form.
\(y =\) <blank>\(-(x-2)^2-7\)</blank>

Question 2

What kind(s) of transformation(s) occur between the graph of the given function and the graph of \(y = x^2\)? Select all that apply.

  • A. A horizontal shift (Correct answer)
  • B. A reflection across the y-axis
  • C. A reflection across the x-axis (Correct answer)
  • D. A vertical shift (Correct answer)