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Answer on Algebra Question for Jon

Question #6039
If you are provided with a quadratic function, how can you determine if there is a minimum or maximum function value? How do you compute this value?
Expert's answer
A value of x at which the function has either a maximum or a minimum is called a critical value.
The critical values determine turning points, at which the tangent is parallel to the x-axis.& The critical values - if any - will be the solutions to the equation& f '(x) =& 0. In case of quadratic function its minimum(or maximum) will be in its vertex. Quadratic function will have minimum if& branches of its graph(parabola)are directed upwords and& minimum otherwise. For example, let's consider function f(x)=x^2+4x
Then its first derivative f'(x)=2x+4
2x+4=0 =>x=-2
f_min(x)=f(-2)=4-8=-4 - minimum value of function, x=-2 - point of minimum
Let's verify our calculations. Take a look at the graph of considered function:

<img style="width: 506px; height: 338px;" src="data:image/png;base64,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" alt="">
As you can see from tha graph, function has its minimum at the point x=-2 and value of minimum is -4. The point of minimum is in the vertex of parabola

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