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 = x^2 + 6x\\)

the vertex is \\((-3, -9)\\)
(type an ordered pair.)

the axis of symmetry is \\(x = -3\\)
(type an equation.)

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

a. the x-intercept(s) is/are \\(x = 0, -6\\)
(use a comma to separate answers as needed. type an integer or a fraction.)
b. there are no x-intercepts.

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

a. the y-intercept(s) is/are \\(y = \\)
(use a comma to separate answers as needed. 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

$$ x = -3 $$

Find the x-intercepts

Using the Quadratic Intercepts Analysis knowledge point

$$
LATEXBLOCK2
$$

Find the y-intercept

Using the Quadratic Intercepts Analysis knowledge point

$$
LATEXBLOCK3
$$

Answer:

Find the y-intercept(s). Select the correct answer below and, if necessary, fill in the answer box to complete your choice.

• A. The y-intercept(s) is/are y = <blank>0</blank> (Correct answer)
• B. There is no y-intercept.