Question

List the key features of the quadratic function y = x^2 - 16.

a) The key features include the vertex, axis of symmetry, and discriminant.
b) The key features include the leading coefficient, constant term, and standard form.
c) The key features include the maximum or minimum value, the direction of the parabola, and the x-intercepts.
d) The key features include the linear coefficient, domain, and range.

Answer 1

The key features of a quadratic function like y = x^2 - 16 include the maximum or minimum value, the direction of the parabola, and the x-intercepts, which for this function are the minimum at (0, -16), an upwards direction for the parabola, and x-intercepts at (4, 0) and (-4, 0).

Step-by-step explanation:

The correct answer to the question about the key features of the quadratic function y = x^2 - 16 is (c): The key features include the maximum or minimum value, the direction of the parabola, and the x-intercepts. For the given function, the vertex acts as the minimum value and it is located at (0, -16), which is also the minimum value since the parabola opens upwards. This is because the coefficient of x^2 is positive. The axis of symmetry is x = 0. The x-intercepts are found by setting y to zero and solving for x, which in this case gives you the solutions x = 4 and x = -4. The key features of a quadratic function are crucial in graphing and understanding the behavior of the function on a two-dimensional (x-y) graph.