The vertex of the graph of the quadratic function g(x) = x^2 – 8x + 6 can be found using the vertex formula or by completing the square.
First, let’s identify the coefficients in the standard form of a quadratic function, which is g(x) = ax^2 + bx + c. Here, a = 1, b = -8, and c = 6.
The x-coordinate of the vertex can be calculated using the formula:
x = -b / (2a)
Plugging in the values:
x = -(-8) / (2 * 1) = 8 / 2 = 4
Now that we have the x-coordinate, we can find the y-coordinate by substituting x back into the function:
g(4) = (4)^2 – 8(4) + 6
Calculating that gives:
Thus, the vertex of the graph is at the point (4, -10).
In conclusion, the vertex of the graph g(x) = x^2 – 8x + 6 is located at (4, -10).