Determine Coordinates: Calculating Point C on f(x) = x² - 6x + 5

We are required to find a particular point C on the graph of the function $f(x) = x^2 - 6x + 5$. Typically, important features of the graph include the vertex or y-intercept.

The function $f(x) = x^2 - 6x + 5$ is a quadratic function in standard form, where $a = 1$, $b = -6$, and $c = 5$. Since point C is labeled near the y-axis, it is likely related to the y-intercept. The y-intercept is found by evaluating the function at $x = 0$.

Calculate the y-intercept by substituting $x = 0$ into the function:

• Substitute: $f(0) = (0)^2 - 6(0) + 5 = 5$

This gives the point on the y-axis where the function intersects, which is point C. Thus, point C is at the coordinates $(0, 5)$.

This point matches choice 2 among the provided choices.

Therefore, the solution to the problem is $(0, 5)$.