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

use the graphing tool to graph the function.

Explanation:

Rewrite the function in vertex form

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

$$
LATEXBLOCK0
$$

Identify the transformations

Using the Graph Transformations knowledge point

• The term \((x - 2)\) represents a horizontal shift right by 2 units.
• The negative sign in front of the squared term represents a reflection across the x-axis.
• The term \(-7\) represents a vertical shift down by 7 units.
• Therefore, the transformations that occur are a horizontal shift, a reflection across the x-axis, and a vertical shift.

Answer:

Question 1

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