9. What is the vertex of the parabola y = x^2 + 4x + 1?:
A. (2, -3)
B. (-2, 3)
C. (2, 3)
D. (-2, -3)
To find the vertex of a parabola in the form of y = ax^2 + bx + c, you can use the following steps:
Step 1: Identify the values of a, b, and c from the equation. In this case, a = 1, b = 4, and c = 1.
Step 2: Calculate the x-coordinate of the vertex. Use the formula x = -b/(2a). Plugging in the values of a and b, we get x = -4/(2*1) = -4/2 = -2.
Step 3: Substitute the x-coordinate of the vertex into the equation to find the y-coordinate. Plugging in x = -2, we get y = (-2)^2 + 4(-2) + 1 = 4 - 8 + 1 = -3.
Therefore, the vertex of the parabola y = x^2 + 4x + 1 is (-2, -3).
So, the correct answer is D. (-2, -3).