Graph: y=f(x)=-x2+3x. Give the coordinates of the vertex, the x-intercepts (if they exist), the y-intercept, the domain, range, max/min value, and the equation of the axis of symmetry.

vertex

x-int.

y-int.

domain

range

max/min

axis of symmetry

- October 28th 2009, 09:57 AMJluse7PLEASE HELP! I dont fully understand how to do this certain problem.
Graph: y=f(x)=-x2+3x. Give the coordinates of the vertex, the x-intercepts (if they exist), the y-intercept, the domain, range, max/min value, and the equation of the axis of symmetry.

vertex

x-int.

y-int.

domain

range

max/min

axis of symmetry - October 28th 2009, 11:18 AMmasters
Hi Jluse7,

You need to translate your functional notation into vertex form. The graph will be a parabola opening downward.

Complete the square:

This tells you that the vertex of your parabola is at

Set f(x) = 0 to find your x intercepts. Use your original function.

Notice, since x = 0, f(0) = 0, thus the y-intercept is 0.

The domain will be all real numbers. There are no restrictions on x.

The range will be

The maximum value will occur at the vertex where .

There is no minimum.

The axis of symmetry is . This is a vertical line which passes through the vertex.