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a) Explain the relationship between the axis of symmetry and the quadratic formula.

b) We know that the quadratic formula can be used to determine the roots of a quadratic function. However, the quadratic formula also reveals how many roots exist without the need to find them. Explain why (not how) we are able to determine the number of roots a quadratic has without actually determining what they are.

Please answer each question by indicating which question you are answering.
Ex: Part A
A) Answer here

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1 answer

  1. you know that x = -b/2a ±√(b^2-4ac)/2a
    so the axis of symmetry is at x = -b/2a, midway between the roots, if any.

    If b^2-4ac is negative, there are no real roots. Thus the name "discriminant," because it allows you to discriminate the number and type of roots.

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