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#### thorpelizts

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- Sep 7, 2012

- 6

How do you prove? Do you find he discriminant? But isnt discriminant for roots only not equations?

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- Sep 7, 2012

- 6

How do you prove? Do you find he discriminant? But isnt discriminant for roots only not equations?

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- Jan 26, 2012

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Otherwise I would say in general that a quadratic function with a negative leading coefficient is a parabola that faces downward and has a maximum point at the vertex.

If the formula for a parabola is given in the form \(\displaystyle y=ax^2+bx+c\) then the vertex is \(\displaystyle x=-\frac{b}{2a}\). Again this requires some context for the course.

- Jan 26, 2012

- 890

This is the standard non-calculus method for finding the maximum/minimum of a quadratic expression:

How do you prove? Do you find he discriminant? But isnt discriminant for roots only not equations?

You first complete the square to get:

\[-3x^2+12x-8=-3(x-2)^2+12-8=-3(x-2)^2 +4\]

Now since the largest \(-3(x-2)^2\) can be is zero the largest the whole thing can be is \(+4\).

CB

Last edited:

- Jan 26, 2012

- 66

It should be recognized as a negative parabola so your job is to find the vertical coordinate of the maximum turning point. Several methods have already been suggested.

How do you prove? Do you find he discriminant? But isnt discriminant for roots only not equations?