Over what interval is the graph of f(x) = -(x + 8)² – 1 decreasing?

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    Answer: The graph of f(x) = -(x + 8)² – 1 is always decreasing because it is a downward-opening parabola.

    Analyzing Quadratic Graphs

    The graph of a quadratic function y = a(x – h)² + k will open upwards if a is positive and downwards if a is negative. For the function f(x) = -(x + 8)² – 1, the coefficient of the x² term is negative, indicating that it opens downwards, and thus it is always decreasing. Understanding the shape and direction of parabolas is fundamental in graph analysis, important in fields ranging from physics to finance, helping to predict and understand behavior.

    FAQ on Analyzing Quadratic Graphs

    What determines the direction a parabola opens?

    The sign of the coefficient ‘a’ in the quadratic formula.

    What is the vertex of a parabola?

    The vertex is the highest or lowest point on a parabola, given by (h, k).

    How do you find the x-intercepts of a parabola?

    Set the quadratic equation equal to zero and solve for x.

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