Answer:
y = (x + 5)^2 - 17
Explanation:
To write the quadratic function y = x^2 + 10x + 8 in vertex form, we need to complete the square. We start by adding and subtracting the square of half of the coefficient of x, which is (10/2)^2 = 25:
y = x^2 + 10x + 8
= (x^2 + 10x + 25) - 25 + 8
= (x + 5)^2 - 17
Therefore, the quadratic function in vertex form is:
y = (x + 5)^2 - 17
The vertex of this parabola is at the point (-5, -17), and the axis of symmetry is the vertical line x = -5. The term (-17) represents the minimum value of the function.