Please help! I am lost in how to figure this out:
That's the same as
Plot some points:
(-2,-4), (-1,4), (0,8), (1,8), (2,4), (3,-4)
and get this graph:
This one has several parts..
The x coordinate of the vertex?
Learn the formula:
The x-coordinate of is
Compare
to
and observe that , ,
Then substitute and get
The y coordinate of the vertex?
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:
The equation of the line of symmetry?
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.
The maximum/minimum of f(x)?
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.
Is the value of maximum or minimum?
It is a maximum as we have just seen.
Thanks!