Determine without graphing, whether the given quadratic functions has a maximum value or a minimum value and then find the value f(x)=x^2-8x

Question

anonymous · Answer

Do you the concept of maxima and minima?

anonymous · Answer

never mind Interrif, I figure the problem out already.. but I do have another question.....

anonymous · Answer

Without calculus, you can complete the square to find the minimum or maximum value.

$$f(x) = x^{2} - 8x$$

$$f(x) = x^{2} - (2)(4x)$$

From this step you should be able to figure out to add and subtract $$4^{2}$$

to the right side.

$$f(x) = x^{2} - (2)(4x) + 4^{2} - 4^{2}$$

$$f(x) = (x-4)^{2} - 16$$

From this equation you can reason that the vertex of the parabola is located at (4, -16).

As for whether it is a maximum or a minimum, you can look at the leading coefficient. In this case, the leading coefficient is +1. Because it is positive, the parabola opens up, and the vertex must be the lowest point on the graph.

anonymous · Answer

Oh darn.