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If a quadratic function has a maximun value that is greater then 0 how many zeros does the function hsve?

User Cvandal
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The quadratic has a maximum y value that is greater than 0. That means that the maximum might be above the x axis . The quadratic has a condition for this to be true. x^2 must be negative. You are being told that the quadratic cuts the x axis twice. Use y = - (x - 3)(x + 2) as an example. It is the graph on the left.

The graph on the right is of two different quadratics.
y = -(x^2 + 5x + 6) [in red]
y = -(x^2 - 5x + 6) [in blue]

Comment
as long as y > 0 with a minus x^2, you cannot draw a quadratic that does not cut the x axis twice. This is not a formal proof of the statement, but it is an indication of what may be proved later on in your course.


If a quadratic function has a maximun value that is greater then 0 how many zeros-example-1
If a quadratic function has a maximun value that is greater then 0 how many zeros-example-2
User Keji
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