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\\)

\\(y = (x+3)^2 - 9\\)
(type an equation. use integers or fractions for any numbers in the equation.)

use the graphing tool to graph the function.

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 = \square\\)
(use a comma to separate answers as needed. type an integer or a fraction.)

b. there are no x-intercepts.

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:

The standard form is <blank>\(y = (x+3)^2 - 9\)</blank>.

The vertex is <blank>\((-3, -9)\)</blank>.

The axis of symmetry is <blank>\(x = -3\)</blank>.

The x-intercept(s) is/are x = <blank>\(0, -6\)</blank>.