Question

Find the maximum y value on the graph of y=f(x) if f(x)=-x^2+4x+1?

Answer 1

Do you know derivatives or the shape of this curve? If you plotted it, you could almost guess the solution. Because there is an x^2 term there, it will be a curve, not a straight line. This means it's "quadratic." There is a formula to solve quadratic equations. Do you know it? Because of the negative sign in front of the quadratic term (i.e. x^2), we know that the graph will point downward. If you plotted this, you'd see it. Now, if you used the quadratic formula, you'll see a term there that looks like -b/2a, this represents where the maximum will occur (which we call the vertex of the parabola).

Read this if you need more information or let me know if you have any questions so far:

http://en.wikipedia.org/wiki/Quadratic_equation

Answer 2

Here is a graph of your function: http://www.wolframalpha.com/input/?i=-x^2%2B4x%2B1 and lot's of other useful information.