Question

find the minimum value of the parabola $y = x^2 + 4x + 2$. simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Complete the square

$y = x^2 + 4x + 2 = (x^2 + 4x + 4) - 4 + 2$

Step2: Simplify the expression

$y = (x + 2)^2 - 2$

Step3: Identify minimum value

Since $(x + 2)^2 \geq 0$, its minimum is 0. Substitute this into the equation: $y = 0 - 2$

Answer:

$-2$