To find the coordinates of the vertex for the quadratic function f(x) = x² + 6x + 13, we can use the vertex formula. The vertex (h, k) of a parabola in the form f(x) = ax² + bx + c is given by:
h = -b / (2a)
Here, a = 1 and b = 6. Plugging in these values:
h = -6 / (2 × 1) = -6 / 2 = -3
Now, to find the corresponding k value, we substitute h back into the original function:
k = f(-3) = (-3)² + 6(-3) + 13
Calculating this step by step:
- (-3)² = 9
- 6(-3) = -18
- So, k = 9 – 18 + 13 = 4
Thus, the coordinates of the vertex are (-3, 4).