Question

Write the quadratic function in standard form to represent a parabola with zeros of -4 and 2 and that passes through the point (1,-15)

Answer 1

Step-by-step explanation:
The first step is to define your variables
h
=
−
4

k
=
2
And we know one set of points on the graph, so
x
=
−
7

y
=
−
34
Next solve the formula for
a

y
=
a
(
x
−
h
)
2
+
k

−
34
=
a
(
−
7
+
4
)
2
+
2

−
34
=
a
(
−
3
)
2
+
2

−
34
=
9
a
+
2

−
36
=
9
a

−
4
=
a
To create a general formula for the parabola you would put in the values for
a
,
h
, and
k
and then simplify.
y
=
a
(
x
−
h
)
2
+
k

y
=
−
4
(
x
+
4
)
2
+
2

y
=
−
4
(
x
2
+
8
x
+
16
)
+
2

y
=
−
4
x
2
−
32
x
−
64
+
2
So the equation of a parabola that has a vertex at
(
−
4
,
2
)
and passes through point
(
−
7
,
−
34
)
is:
y
=
−
4
x
2
−
32
x
−
62