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\\

rewrite \\(y = x^2 + 6x\\) in standard form.

\\(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.

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

$$
LATEXBLOCK1
$$

Determine the axis of symmetry

Using the Axis of Symmetry knowledge point

$$ x = -3 $$

Find the intercepts

Using the Quadratic Intercepts Analysis knowledge point

$$
LATEXBLOCK2
$$

Graph the function

Using the Parabola Graphing knowledge point
We plot the vertex at \((-3, -9)\), the y-intercept at \((0, 0)\), and the other x-intercept at \((-6, 0)\) to sketch the upward-opening parabola.

Answer:

• Standard Form: \(y = (x+3)^2 - 9\)
• Vertex: \((-3, -9)\)
• Axis of Symmetry: \(x = -3\)
• x-intercepts: \((0, 0)\) and \((-6, 0)\)
• y-intercept: \((0, 0)\)