Answer:
y
=
−
3
x
2
+
30
x
−
71
Explanation:
the equation of a parabola in
vertex form
is.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
∣
∣
∣
2
2
y
=
a
(
x
−
h
)
2
+
k
2
2
∣
∣
∣
−−−−−−−−−−−−−−−−−−−−−
where
(
h
,
k
)
are the coordinates of the vertex and a
is a multiplier
here
(
h
,
k
)
=
(
5
,
4
)
⇒
y
=
a
(
x
−
5
)
2
+
4
to find a substitute
(
7
,
−
8
)
into the equation
−
8
=
4
a
+
4
⇒
a
=
−
3
⇒
y
=
−
3
(
x
−
5
)
2
+
4
←
in vertex form
distributing and simplifying gives
y
=
−
3
(
x
2
−
10
x
+
25
)
+
4
y
=
−
3
x
2
+
30
x
−
75
+
4
⇒
y
=
−
3
x
2
+
30
x
−
71
←
in standard form
Step-by-step explanation:
