Specify the abscissa of the vertex of the parabola y = x ^ 2 + 8x + 17.

The vertex of the parabola is the extremum point of the function. To find it, you need to find the derivative of this function and equate it to zero:

Y = X² + 8 x X + 17;

Y ′ = 2 x X + 8.

We equate it to zero:

2 x X + 8 = 0;

2 x X = – 8;

X = – 4.

Let’s check if this is so. Let’s substitute in the function the values – 3; – 4; – five:

Y (- 3) = 9 – 24 + 17 = 2;

Y (- 4) = 16 – 32 + 17 = 1;

Y (- 5) = 25 – 40 + 17 = 2.

We see that at X = – 4 the function takes the smallest value, that is, this is the vertex of the parabola.

Answer: the abscissa of the vertex of the parabola is X = – 4.