A classmate said that the vertex of y -5(x +2)-6 is (2, 6). What mistake did your classmate make? What is the correct vertex?
1 answer:
<u>Answer:</u>
The correct vertex said by classmate is (-2, -6).
<u>Solution:</u>
Given, equation of parabola is
We have to find mistake did by the classmate and rectify it.
Now we know that, general form of an parabolic equation is
where a is an constant and (h, k) is vertex point of the parabola.
So, now by comparison of given parabola equation with general form, h = -2 and k = -6
Then, vertex point will be (-2, -6).
We can say that, classmate mistook the general form as
So he got h = 2 and k = 6.
Hence, the correct vertex is (-2, -6).
You might be interested in
Lagrange multipliers:
(if 
)
(if )
(if 
)
In the first octant, we assume
, so we can ignore the caveats above. Now,
so that the only critical point in the region of interest is (1, 2, 2), for which we get a maximum value of
.
We also need to check the boundary of the region, i.e. the intersection of
with the three coordinate axes. But in each case, we would end up setting at least one of the variables to 0, which would force 
, so the point we found is the only extremum.
In the first octant, we assume
so that the only critical point in the region of interest is (1, 2, 2), for which we get a maximum value of
We also need to check the boundary of the region, i.e. the intersection of