Final answer:
The vertex of the parabola y = -1/18x² + x is found using the formula -b/(2a) to locate the x-coordinate and then substituting x back into the equation to find the y-coordinate. The vertex is (9, 4.5).
Step-by-step explanation:
To find the vertex of the parabola represented by y=-1/18+x²+x, we first need to rewrite the equation in vertex form, y = a(x - h)² + k, where (h, k) is the vertex of the parabola. However, the equation provided seems to have a typo, with the term -1/18 appearing awkwardly. Assuming the correct equation is y = -1/18x² + x (which makes more sense for a quadratic expression), we can use the formula -b/(2a) to find the x-coordinate of the vertex.
The coefficient 'a' is -1/18 and 'b' is 1. Plugging these values into the formula, we get x = -1 / (2*(-1/18)) = -1 / (-1/9) = 9. To find the y-coordinate of the vertex, we substitute x back into the original equation: y = -1/18*(9)² + 9. After simplification, we get y = -4.5 + 9 = 4.5.
Therefore, the vertex of the graph of the equation y = -1/18x² + x is (9, 4.5).