find the coordinates of the vertex of the quadratic function y=x^2+4x+6
Answers
Answer:
You have a quadratic function in the form
y
=
a
x
2
+
b
x
+
c
which represents, graphically, a PARABOLA.
You can start by observing that the coefficient of the
x
2
is positive so that your parabola has an upward concavity, i.e., has a shape like a U.
Then you need to determine 3 sets of coordinates that characterize your parabola:
1) The Vertex: this is the lowest point of your parabola (the bottom of your U).
to find its coordinates (
x
v
and
y
v
) you use the fact that:
x
v
=
−
b
2
a
and
y
=
−
Δ
4
a
Where
Δ
=
b
2
−
4
a
c
2) Crossing point with the
y
axis:
This point has coordinates: (
0
,
c
)
3) Crossing point(s) with the
x
axis:
These are obtained putting
y
=
0
and solving the corresponding second degree equation:
a
x
2
+
b
x
+
c
=
0
If the equation doesn't have solutions (
Δ
<
0
) your parabola doesn't cross the
x
axis.
If
Δ
=
0
your vertex is also the point of crossing with the
x
axis.
In our case we have:
enter image source here
