Function 1
First step: Finding when
is minimum/maximum
The function has a negative value
hence the
has a maximum value which happens when
. The foci of this parabola lies on
.
Second step: Find the value of y-coordinate by substituting
into
which give
Third step: Find the distance of the foci from the y-coordinate
- Multiply all term by -1 to get a positive
- then manipulate the constant of y to get a multiply of 4
So the distance of focus is 0.25 to the south of y-coordinates of the maximum, which is
Hence the coordinate of the foci is (2, 11.75)
Function 2:
The function has a positive
so it has a minimum
First step -
Second step -
Third step - Manipulating
to leave
with constant of 1
- Divide all terms by 2
- Manipulate the constant of y to get a multiply of 4
So the distance of focus from y-coordinate is
to the north of
Hence the coordinate of foci is (-4, -14+0.125) = (-4, -13.875)
Function 3:
First step: the function's maximum value happens when
Second step:
Third step: Manipulating
- Divide all terms by -2
- Manipulate coefficient of y to get a multiply of 4
So the distance of the foci from the y-coordinate is -
south to y-coordinate
Hence the coordinate of foci is (1.25, 17)
Function 4: following the steps above, the maximum value is when
and
. The distance from y-coordinate is 0.25 to the south of y-coordinate, hence the coordinate of foci is (8.5, 79.25-0.25)=(8.5,79)
Function 5: the minimum value of the function is when
and
. Manipulating coefficient of y, the distance of foci from y-coordinate is
to the north. Hence the coordinate of the foci is (-2.75, -10.125+0.125)=(-2.75, -10)
Function 6: The maximum value happens when
and
. The distance of the foci from the y-coordinate is
to the south. Hence the coordinate of foci is (1.5, 9.5-0.125)=(1.5, 9.375)
