Answer: To find the vertex of a quadratic equation, you can either use the vertex formula, or complete the square. The vertex formula is:
�
=
−
�
2
�
x=−2ab
where
�
a and
�
b are the coefficients of the
�
2
x2 and
�
x terms in the equation. Once you find the value of
�
x, you can plug it back into the equation to get the value of
�
y. The vertex is then given by the ordered pair
(
�
,
�
)
(x,y).
Using this method, we can find the vertex of
�
(
�
)
=
−
3
�
2
+
18
�
+
2
g(x)=−3x2+18x+2 as follows:
Identify the values of
�
a and
�
b. In this case,
�
=
−
3
a=−3 and
�
=
18
b=18.
Plug them into the vertex formula and simplify:
�
=
−
�
2
�
x=−2ab
�
=
−
18
2
(
−
3
)
x=−2(−3)18
�
=
−
18
−
6
x=−−618
�
=
3
x=3
Plug the value of
�
x into the equation to get the value of
�
y:
�
=
�
(
�
)
y=g(x)
�
=
�
(
3
)
y=g(3)
�
=
−
3
(
3
)
2
+
18
(
3
)
+
2
y=−3(3)2+18(3)+2
�
=
−
27
+
54
+
2
y=−27+54+2
�
=
29
y=29
Write down the vertex as an ordered pair:
(
3
,
29
)
(3,29).
Therefore, the vertex of
�
(
�
)
=
−
3
�
2
+
18
�
+
2
g(x)=−3x2+18x+2 is
(
3
,
29
)
(3,29). This means that the parabola has a maximum point at
(
3
,
29
)
(3,29), and its axis of symmetery