To find the coordinates of the vertex of the quadratic function f(x) = x² + 10x + 3, we can use the vertex formula. The x-coordinate of the vertex for any quadratic in the form f(x) = ax² + bx + c can be found using the formula:
x = -b / (2a)
In our case, the coefficients are a = 1 and b = 10. Plugging these values into the formula gives us:
x = -10 / (2 * 1) = -10 / 2 = -5
Now that we have the x-coordinate, we need to find the y-coordinate by plugging x back into the function:
f(-5) = (-5)² + 10(-5) + 3
f(-5) = 25 – 50 + 3 = -22
So, the coordinates of the vertex are (-5, -22). This means the vertex of the function f(x) = x² + 10x + 3 is located at the point (-5, -22).