Question

Transform the quadratic equation from vertex form to standard form and state the axis of symmetry.

y
=
3
(
x
+
3
)
2
−
4

(1 point)
Responses

y
=
x
2
+
6
x
+
5
and
x
=
3
y equals x squared plus 6 x plus 5 and x equals 3

y
=
3
x
2
+
18
x
+
23
and
x
=
−
3
y equals 3 x squared plus 18 x plus 23 and x equals negative 3

y
=
3
x
2
+
18
x
+
23
and
x
=
3
y equals 3 x squared plus 18 x plus 23 and x equals 3

y
=
3
x
2
+
18
x
+
31
and
x
=
−
3
y equals 3 x squared plus 18 x plus 31 and x equals negative 3
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Answer 1

To transform the quadratic equation from vertex form to standard form and find the axis of symmetry, we start with the given vertex form of the equation:

\[
y = 3(x + 3)^2 - 4
\]

1. **Expand the equation** to convert it to standard form (which is \(y = ax^2 + bx + c\)):
- First, expand \((x + 3)^2\):
\[
(x + 3)^2 = x^2 + 6x + 9
\]
- Now substitute this back into the equation:
\[
y = 3(x^2 + 6x + 9) - 4
\]
- Distributing the \(3\):
\[
y = 3x^2 + 18x + 27 - 4
\]
- Combine like terms:
\[
y = 3x^2 + 18x + 23
\]

2. **Identify the axis of symmetry**. The vertex form gives the vertex directly. The x-coordinate of the vertex \((-3)\) is used to find the axis of symmetry, which is:
\[
x = -3
\]

So, the final answer is:
\[
y = 3x^2 + 18x + 23 \quad \text{and} \quad x = -3
\]

Thus, the correct response is:
\[
y = 3x^2 + 18x + 23 \quad \text{and} \quad x = -3
\]