Final answer:
The x-intercepts of the function are 1 and 5, the y-intercept is (0, 5), the vertex is (3, -4), and the axis of symmetry is x = 3.
Step-by-step explanation:
The x-intercepts are the points where the graph of a function intersects the x-axis. To find the x-intercepts, we set y = 0 and solve for x. For the function f(x) = x² - 6x + 5, we get x² - 6x + 5 = 0. Factoring or using the quadratic formula, we find that the x-intercepts are x = 1 and x = 5.
The y-intercept is the point where the graph intersects the y-axis. To find the y-intercept, we set x = 0 and evaluate the function. For the given function, f(0) = 5, so the y-intercept is (0, 5).
The vertex is the point where the graph reaches its minimum or maximum value. The x-coordinate of the vertex is given by the formula x = -b/2a, where a and b are coefficients of the quadratic function. For the given function, x = -(-6)/(2(1)) = 3. To find the y-coordinate of the vertex, we substitute x = 3 into the function: f(3) = 3² - 6(3) + 5 = -4. Therefore, the vertex is (3, -4).
The axis of symmetry is a vertical line that passes through the vertex. For the given function, the axis of symmetry is x = 3.