Question

Find the maximum value of the function given by
f(x) = -3x^2 + 6x +1

Answer 1

the graph looks like that

Answer 2

the vertex of any parabola of the form y=ax^2+bx+c is (-b/(2a))
find the vertex using this formula
thats the x value
plug the x value into the original equation, this will give the maximum or minimum (the y value at the vertex)

Answer 3

You can get the maximum value either by algebra (completing the square), or by differential calculus. I could show you either method if you like.

Answer 4

sure, that will be great

Answer 5

So, which method is it that you need to see? If you are in algebra, your teacher probably wants you to complete the square and use the vertex form of the equation of the parabola. If you are in calculus, we can start with the first derivative and a discussion of the concavity.

Answer 6

this is pre-calculus class

Answer 7

f(x) = -3x^2 + 6x +1 = -3(x^2 - 2x) + 1 = -3(x^2 - 2x + 1) + 1 + 3 = -3(x - 1)^2 + 4. So, the max is at f(1) = 4 and the axis of symmetry is at x = 1. What is more important than just getting the answer though is an explanation of each of these steps. I encourage you to study these and ask me questions now.

Answer 8

Is this making sense to you? Take that equation string from my last post and ask me about anything that seems confusing.

Answer 9

This makes sense