Put the quadratic into vertex form and state the coordinates of the vertex.y, equals, x, squared, plus, 2, x, plus, 17y=x 2 +2x+17

To put the quadratic equation into vertex form, we need to complete the square. The vertex form of a quadratic is y=a(x-h)²+k, where (h,k) is the vertex of the parabola.

The given equation is y = x² + 2x + 17.

Step 1: Group the x terms together: y = (x² + 2x) + 17.

Step 2: To complete the square, we need to add and subtract the square of half the coefficient of x inside the bracket. Half of 2 is 1, and 1² = 1. So, we add and subtract 1 inside the bracket: y = (x² + 2x + 1 - 1) + 17.

Step 3: Simplify the equation: y = [(x + 1)² - 1] + 17.

Step 4: Simplify further to get the equation in vertex form: y = (x + 1)² + 16.

So, the given quadratic equation in vertex form is y = (x + 1)² + 16.

The coordinates of the vertex (h, k) are (-1, 16).