SOLUTION: Please help! I am lost in how to figure this out: f(x)= -2x^2+2x+8 This one has several parts.. The x coordinate of the vertex? The y coordinate of the vertex? The e

That's the same as



Plot some points:

(-2,-4), (-1,4), (0,8), (1,8), (2,4), (3,-4)

and get this graph:

Learn the formula:

The x-coordinate of  is 

Compare

to


and observe that , , 

Then substitute and get

Learn the rule: To get the y-coordinate of the vertex,
after finding the x-coordinate of the vertex, substitute
the value of the x-coordinate of the vertex x in the original 
equation:







So the y coordinate of the vertex is  or 

That makes the vertes (,), or (0.5,8.5)

and we see that looks right according to the graph:

Learn the rule that the equation of the line of symmetry
is always the vertical line whose equation is

x = the x-coordinate of the vertex

So the axis of symmetry has the equation 

 or 

which is a vertical line  a unit right of the y-axis
and parallel to it (vertical), and when we graph it (in green,



and we see that this vertical line whose equation is ,
bisects the parabola. 

Learn that the maximum or minimum value is the y-coordinate of
the vertex.

The maximum or minimum point is the same as the vertex.

To determine whether or not it is a maximum or a minimum
we need to know whether the parabola opens upward or downward.
To determine this we look at the coefficient of .
If it is positive then the parabola opens upward and the
vertex is a minimum point. If it is negative, the parabola 
opens downward and the vertex is a maximum.  



Here we see that the coefficient of  is negative and
that the parabola opens downward, so the vertex is a maximum.
We knew it opened downward because we graphed it, but we
would have known it opened downward even if we had not
graphed it because the coefficient of  is negative. 

It is a maximum as we have just seen.



Thanks!