Graph parabola by completing the square. Label the vertex, the axis of symmetry, and two other points for the equation y = x2 + 6x + 4.

Step 1: Rewrite the equation in the form of y = a(x-h)² + k. This is the vertex form of a parabola where (h, k) is the vertex of the parabola.

The given equation is y = x² + 6x + 4.

Step 2: Group the x terms together.

y = (x² + 6x) + 4

Step 3: Complete the square. To do this, take the coefficient of the x term (which is 6 in this case), divide it by 2 and square the result.

(6/2)² = 9

Add and subtract this number inside the parenthesis.

y = (x² + 6x + 9 - 9) + 4

Step 4: Simplify the equation.

y = (x² + 6x + 9) - 9 + 4

y = (x + 3)² - 5

Now, the equation is in the form y = a(x-h)² + k.

Step 5: Identify the vertex, the axis of symmetry, and two other points.

The vertex (h, k) is (-3, -5).

The axis of symmetry is x = -3.

To find two other points, you can choose any x-values, plug them into the equation and solve for y. For example, if x = -4, then y = (-4 + 3)² - 5 = 4. So, (-4, 4) is a point on the parabola. If x = -2, then y = (-2 + 3)² - 5 = -4. So, (-2, -4) is another point on the parabola.

Step 6: Plot these points on a graph and draw the parabola.