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\\

the vertex is \\((2, -7)\\).
(type an ordered pair.)

the axis of symmetry is \\(x = 2\\).
(type an equation.)

find the x-intercept(s) of the parabola. choose the correct answer below and, if necessary, fill in the answer box to complete your choice.

a. the x-intercept(s) is/are \\(x = \\).
(use a comma to separate answers as needed. type an integer or a fraction.)
b. there are no x-intercepts.

find the y-intercept. choose the correct answer below and, if necessary, fill in the answer box to complete your choice.

a. the y-intercept is \\(y = \\).
(type an integer or a fraction.)
b. there is no y-intercept.

Explanation:

Convert to vertex form

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

$$
LATEXBLOCK0
$$

Identify the vertex

Using the Vertex Form of a Quadratic knowledge point

$$
LATEXBLOCK1
$$

Find the axis of symmetry

Using the Axis of Symmetry knowledge point

$$
LATEXBLOCK2
$$

Determine the x-intercepts

Using the Quadratic Intercepts Analysis knowledge point

$$
LATEXBLOCK3
$$

Since a squared real number cannot be negative, there are no real solutions. Thus, there are no x-intercepts.

Determine the y-intercept

Using the Quadratic Intercepts Analysis knowledge point

$$
LATEXBLOCK4
$$

Answer:

Question 1

The vertex is <blank>\((2, -7)\)</blank>.

Question 2

The axis of symmetry is <blank>\(x = 2\)</blank>.

Question 3

• A. The x-intercept(s) is/are x =
• B. There are no x-intercepts. (Correct answer)

Question 4

• A. The y-intercept is y = <blank>-11</blank> (Correct answer)
• B. There is no y-intercept.