Final Answer:
The vertex is (2, -4), the axis of symmetry is x = 2, the minimum value is -4, and the y-intercept is -2.
Step-by-step explanation:
The vertex of a parabola is the point where the curve changes direction from opening upwards to opening downwards (or vice versa). The axis of symmetry is a vertical line that passes through the vertex. The minimum value of a quadratic function is the y-coordinate of its vertex if the parabola opens upwards, and the maximum value is the y-coordinate of its vertex if the parabola opens downwards. The y-intercept is the point where the parabola crosses the y-axis.
To find the vertex, we can rewrite the given equation in vertex form. Completing the square, we get:
y = x² - 4x - 2
= x² - 4x + 4 - 2 - 4
= (x - 2)² - 6
= (x - 2)² + 1.75
Therefore, the vertex is (2, 1.75), which means the axis of symmetry is x = 2. Since the parabola opens upwards, the minimum value is 1.75. Finally, setting x = 0 in the original equation, we get y = -2, so the y-intercept is (0, -2).