Final answer:
To find the x and y intercepts of the quadratic function, you set the other variable to zero and solve. The vertex form is found by completing the square, and the vertex can be identified as a minimum or maximum based on the sign of the coefficient of x². In this function, the vertex is a minimum.
Step-by-step explanation:
To find the x and y intercepts algebraically for the quadratic function f(x) = 0.20x² - 1.6x - 1, we set y and x to zero respectively and solve the equations.
To find the vertex form of f, we complete the square. The formula for vertex form is f(x) = a(x - h)² + k, where (h, k) is the vertex.
For the vertex and whether it is a maximum or minimum, we look at the coefficient of x². If a is positive, the parabola opens upwards, and the vertex is a minimum. If a is negative, the parabola opens downwards, and the vertex is a maximum. Since the coefficient of x² in f(x) is positive (0.20), the vertex represents a minimum.
To find the exact value of the vertex, we use the formula h = -b/(2a) and k = f(h). Inserting the values into the formula gives us the coordinates of the vertex.