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    Quadratic equations, discriminant, and graph

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    When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative.

    Create three unique equations where the discriminant is positive, zero, or negative. For each case, explain what this value means to the graph of y = ax2 + bx + c.

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    https://brainmass.com/math/basic-algebra/quadratic-equations-discriminant-and-graph-129946

    Solution Preview

    When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative.

    Create three unique equations where the discriminant is positive, zero, or negative. For each case, explain what this value means to the graph of y = ax2 + bx + c.

    (1) Discriminant is positive

    b2 - 4ac > 0

    The discriminant is positive for a = 1, b = 3, and c = 1 (32 - 4*1*1 = 9 - 4 = 5 > 0). The equation would be:

    y = x2 + ...

    $2.49

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