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Let’s check out your problem:
Find the equation of the
axis of symmetry
of the following parabola algebraically.
\newline
y
=
−
3
x
2
+
18
x
−
21
y=-3 x^{2}+18 x-21
y
=
−
3
x
2
+
18
x
−
21
\newline
Answer:
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Math Problems
Algebra 2
Find the axis of symmetry of a parabola
Full solution
Q.
Find the equation of the axis of symmetry of the following parabola algebraically.
\newline
y
=
−
3
x
2
+
18
x
−
21
y=-3 x^{2}+18 x-21
y
=
−
3
x
2
+
18
x
−
21
\newline
Answer:
Identify Coefficients:
The equation of a parabola in the form
y
=
a
x
2
+
b
x
+
c
y = ax^2 + bx + c
y
=
a
x
2
+
b
x
+
c
can have its axis of symmetry found using the formula
x
=
−
b
2
a
x = -\frac{b}{2a}
x
=
−
2
a
b
.
Apply Formula:
First, identify the coefficients
a
a
a
and
b
b
b
from the given
quadratic equation
y
=
−
3
x
2
+
18
x
−
21
y = -3x^2 + 18x - 21
y
=
−
3
x
2
+
18
x
−
21
. Here,
a
=
−
3
a = -3
a
=
−
3
and
b
=
18
b = 18
b
=
18
.
Calculate Axis of Symmetry:
Now, apply the formula for the axis of symmetry using the values of
a
a
a
and
b
b
b
.
x
=
−
b
2
a
=
−
18
2
×
−
3
=
−
18
−
6
=
3.
x = \frac{-b}{2a} = \frac{-18}{2 \times -3} = \frac{-18}{-6} = 3.
x
=
2
a
−
b
=
2
×
−
3
−
18
=
−
6
−
18
=
3.
Final Result:
The equation of the axis of symmetry is therefore
x
=
3
x = 3
x
=
3
.
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