SOLUTION: I need help solving the quadratic function,For Each Funtion:(a) determine whether the graph opens down or up, (b) find the axis of symmetry, (c)find the vertex, (d)find the y-inter

Question 214894: I need help solving the quadratic function,For Each Funtion:(a) determine whether the graph opens down or up, (b) find the axis of symmetry, (c)find the vertex, (d)find the y-intercept,(e) find the zeros, and (f) graph the function
the equation is: -x(x-3)
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
For:
rewrite as
Find:
a) The graph opens downward as indicated by the negative value of the term.
b) The axis of symmetry (AOS) is given by:
where: a = -1 and b = 3.

This is the equation of the AOS.
c) The vertex is lies on the AOS and is found by using the equation of the AOS for the x-coordinate, then substituting this into the given quadratic equation to solve for the corresponding y-coordinate.
Substitute
Evaluate.

The vertex is at: (3/2, 9/4)
d)
The y-intercept is found by setting x = 0 in the given quadratic equation and solving for y.
Substitute x = 0.

The y-intercept is at: (0, 0)
e)
The zeros are found by setting the given quadratic equation equal to zero and solving.
Factor a -x.
Apply the zero product rule:
or so that...
or
The zeros are at (0, 0) and (3, 0)
f)
Graph:

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